If the instructions given in this article are followed carefully, even someone new to soldering should be quite competent with a few minutes practice, it's really not difficult at all. If you dont want to take the time to read all the details, I have put the main points in bold at the end of each section.
Step 1: Soldering Iron
My advice would be to spend your money on a good fixed temp. iron, it will probably cost you at least as much, even a bit more than one of the cheap adjustable temp. irons. You can always build a temp. control unit for your iron later if you want. You don't need adjustable temp. to do fine work though, if you put a smaller tip in an iron it doesn't transfer as much heat, and most people will only want to go to a fine tip if they are working with surface mount components, and even then some wont go to a fine tip.
The iron I like is the one in the photo, it's a 'Goot' made in Japan, has a ceramic heating element and will go from cold to ready to solder in under 30 seconds. This one is actually 46W and most people will want something around 30 to 40W for general work. But I love the control this iron has, I can solder the most delicate IC and go straight to heavy gauge lugs with the same set-up.
I think some people use underpowered irons with very fine tips, thinking this will be delicate, but end up holding the iron on the part for half a minute to get it to solder, and still get a weak joint. You should only have to hold the iron on something like an IC pin for about 2 or 3 seconds.
If you switch to a fine tip because you want to neaten up your PCB work, for example you're getting solder bridges between pads or IC pins, you will probably find it doesn't help very much. Instead you might find yourself having to hold the iron on longer because it wont heat up enough, and the solder wont flow properly. The tip probably isn't your problem, and you might find switching to thinner solder will help more. Using thinner solder makes it much easier to control how much solder you feed into the joint, if you are using around 1mm diameter solder, try switching to about 0.5mm diameter, but keep the normal size tip.
To sum up: Get a decent soldering iron with the right size tip.
Step 2: Additional Tools
I know lead is bad for you and it's going to be banned in some countries, my advice: stock up on 60/40 solder while you still can. If you want to use 'lead free' solder you might want to get advice from someone who uses it, most of the information here will still apply, you will need more heat though. Of course be safe with it, wash your hands after woking, and don't breath in the fumes, this goes for all types of solder.
A couple of other things you should be aware of if you are thinking about going lead-free. There has been some suggestion that lead-free soldering might be more toxic than leaded soldering, especially at home where you don't always have industrial extraction proceedures. The problem is the higher temp. required results in more fumes from the flux and this is the biggest concern with soldering, not ingesting the lead (unless you are particularly hungry I suppose). Did you think they were phasing out leaded solder to protect hobbyists? it's mostly environmental concerns due to contamination from the lead by industry and when the products end up in land fill. Also if you have to rework lead-free joints you might have problems with tracks lifting on the PCB due to the extra heat required. Lead-free solder gives you dull looking joints, with leaded solder this is normally a sign of a weak joint, so just be aware of this. Do your research and make an informed choice, then do whatever you are comfortable with.
The other things you will need is one of those steel scouring pads or the same thing in brass (sold as solder tip cleaners in the shops), forget the wet sponge, it cools the tip too much and doesn't clean it as nicely. The type of scouring pad you need is those ones that look like they are made out of metal shavings (swarf), not steel wool. I will go into tip cleaning in more detail later as it is very important, never file or use rough sand paper to clean your tip.
You should have a decent holder for your iron, and a tin of tip refresher is well worth the money, not essential, but very very handy. It contains flux and solder type material and cleans and 'tins' your tip in one quick dip of a hot tip. I will go into 'tinning' the tip in more detail later also, it kind of goes together with tip cleaning.
Another tool I can't do without is a solder sucker. I find it's the best way to desolder, I have never like the braid wick method, but I know some people like to use both. I really think a begginer should get at least some kind of solder sucker straight away, It will leave you a nice clean hole and component when you need to re-work something.
Of course other things will help with soldering, such as a well lit work area and things to hold your work in place. Locking tweezers are helpful here and a piece of scrap timber is very handy. I have some holes drilled in a piece that I can press the shaft of potentiometers into to hold them while soldering on wires. Some larger holes hold switches etc. and a thin deep groove made with a saw blade is good for slotting PCBs into when I want to solder hookup wires into the board and such like.
To sum up: Use thin electrical solder, a holder for your iron and a tip cleaning pad (scour)
Step 3: The Method
Modern soldering iron tips tend to have special coatings, this is good because it prevents the oxidising as quickly as they used to. This coating is the reason I say you should never file or sand your tip to clean it, once you start that down that route, you will probably have to keep doing it every so often and the tip will be worn out quite quickly. If you look after the tip, it will last a long time.
Now this oxidisation happens quickly when the tip is hot, you can see it because the tip goes from shiny silver to dark and dull, it actually goes quite grey in colour and can almost become black. Now the problem is this layer of oxidation reduces heat transfer. Some people don't realise just what an effect this has and keep trying to solder with the iron in that state. The problem is, you will struggle to make a single solder joint with a tip like that. The secret is to clean it before every joint. Well sometimes you can do a few joints straight after each other and I would usually at least do both wires of a resistor for instance, but you can't just keep soldering without cleaning the tip.
Now cleaning can just mean wiping the tip on your scouring pad a couple of times, so no big deal. But if the irons been sitting for a few minutes you need to go a bit further. You need to clean and then 'tin' the tip. The 'tinning' prevents the oxidation of the tip and to do it the tip needs to be hot and clean. So you pick up your hot iron, wipe the tip on the scouring pad a few times and then immediately melt solder onto the tip to tin it. Don't be shy with the solder, it's cheap and it will drop of the tip as you do it, but some will stick, kind of 'paint' the tip with solder and then wipe the excess on your scour, then do your solder joints straight away. If you put the iron down for a minute after tinning it, you will probably just need to wipe it on the scouring pad again and then you can solder. But wait too long and you will need to clean and tin it again. This is why it's a good idea to load a board up with say all the resistors and then solder them all in at once instead of putting one in, solder it, put the next one in etc. That way you can do a few joints, wipe clean and do a few more etc. By the way, you should tin a new tip the first time you use it, before the iron gets hot for the first time the tip will be shiny, it heats up and starts going dark, clean it and tin it.
It's not really that difficult and with practice it will become second nature, you will get to know when you need to tin the tip and when you can get away with just wiping it. Be careful though wiping it enough will always clean it, but it shoud be shiny after wiping it, or it will oxidise very quickly. Now that tip refresher I mentioned is great for this, instead of tinning the tip the long way, you just dip it into the solid refresher, it melts and cleans and tins the tip instantly and you just give it a quick wipe on the scourer and keep going. I find the tip refresher lasts longer between tinning than using solder, so its worth the little bit it costs. Plus it lasts for a long time. Check the close up picture of the tip, the top one is oxidised the one below is after tinning, it should look like this whenever you go to solder.
Now the idea with soldering is you want to get both of the things you are joining hot enough and then introduce solder. Don't load up the tip with solder and try to transfer it to the joint. You should touch both pieces you want to join with the tip at the same time and hold it there for a couple of seconds to allow them to heat up. Now the best way to work out what you should be heating is to remember a simple rule.
Solder will always flow towards heat.
So hold your iron on the join for a second or two, then introduce solder into the join, it will melt when it touches the iron, as soon as you see the solder flow into the joint, lift the soldering iron away. Don't jerk it away, just lift it off.
Now to do this well you need to have everything secured in place so you can hold the iron in one hand and the solder in the other. No balancing tricks (until you know what your doing and can get away with it). This requires having everything held in place by its own weight or under tension or with a clamp, or whatever, no chasing parts around the bench with a hot iron.
By the way, check the pictures I put on this step of an example joint, it should look something like this (not great as I was trying to take pictures at the same time) it should have a slight concave to the solder join and be smooth. In the second picture you can kind of see how I'm holding the tip onto the copper pad and also against the resistor lead close to the pad. Notice the size of tip I'm using, it's the standard tip the iron comes with, not exceptionally fine. But this isn't a large component, its a small (1/4 watt) resistor.
To sum up: keep the tip clean and tinned for every joint, solder always flows to heat.
Step 4: Some Tips
If you think you might be in danger of damaging a sensitive part with heat, use a heat sink. This can be as simple as clipping an aligator clip or tweezers onto the lead between the solder joint and the component.
If your doing a board with lots of components, just think about the order you put them in. Smaller parts like resitors and diodes first (if they are laid flat), this way you can flip the board over and they will be held in place, sandwiched between the board and work surface. Then the next tallest components and so on. Some parts will probably need other solutions. I don't like bending leads too much to hold parts it place, it makes it harder to get a nice joint.
While I'm on the subject of PCBs, if you drill your own boards, don't make the holes too much bigger than the component leads, a tight fit not only holds them in place better, it leaves a smaller gap. A large gap is much harder to fill with solder. You can get cretive holding parts in place and there are a lot of tricks that I wont get into at this point. If you solder something and find the join is not the best, say its only soldered on one side, use heat to bring the solder over to where it's needed, you might need to add a bit more solder.
If you are soldering wire to something, tin the wire and the lug you are soldering it to. The way I do this is strip off the insulation at the end of the wire. If its multi strand I twist the wires together so they are tightly packed. You can put the wire into some tye of holder or whatever, but I hold the wire and the solder in one hand, with the solder parallel to the wire. In fact it is touching the wire, sitting on top of the bare wire like I am going to thread the wire and solder through the same imaginary needle. Then I touch the bare wire from the bottom with the soldering iron and run the iron back are forth along the length of bare wire. The solder melts and flows into the wire. The wire doesn't increase in diameter much but the strands are held together by the solder and they are coated. With practice it takes a few seconds.
Don't clean excess solder off your iron before you turn it off and put it away, solder on the tip will protect it until you're ready to use it again.
I might add some more tips when I have time, I hope you found something helpful, it took a while to write. Now go use your mad skills to impress your friends and make some nice electronic gear.
To sum up: you are ready grasshopper, go forth and solder