Ok so a few of the things here have been posted, most using higher end camera with full creative controls, it isn't necessary Throughout this I used a five year old compact, though some of the pictures have been taken on the fuji because I didn't have the stuff lying about or to hand.
Step 1: Your Camera You Say?
So have a mess about with the settings on your camera, what can you change?
Does it have a manual setting? If so you're in luck, this gives you loads of control over your photos, if not don't fret about it, you just need to take advantage of the presets in the camera such as night mode.
Do you have macro? It's a big help in taking close ups, especially those going towards instructables...
If it has macro does it have fixed or auto-focus, 99% of the time yes but many cameras do appear with two lens focus presets, usually you have to twist part of the lens or some such to use them though. Manual focus is also really great for close ups because sometime the autofocus is simply no good.
Zoom? Not a neccessity but a nice feature to have.
Ok now you should have an idea of what your doing having just hoked through most of the settings, you can probably see which instructions to follow for camera settings.
Step 2: Long Exposures 1.
So this is the start of the instructable and first up is the cover shot (so called)
A very simple thing to do really, you need a vaguely dark room, I could still see just fine for this shot, oh and probably the camera and a lighter I suppose.
Your settings... So on your camera if you have manual you will need to set the Iso to a nice medium level, enough to capture the pretty bit without the background being grainy, Max aperture if you can't find the setting, don't worry they're usually in the right range anyway and of course shutter speed, this is the variable bit, in the photo below it's only a second long and I sparked the lighter twice for flame and sparks. You can easily go for anywhere between 0.5s and 2.0s shutter speed and it'll come out nicely, above 2.0s the sparks lose some brilliance.
I don't have these options on my camera... Well you'll need a darker room and switch to night mode, remember flash turned off, you should have control over that, if not you could do it outside or buy an new camera. Now meter the shot (half button press) in darkness for a longer shutter speed, get ready to spark the lighter and start sparking from the button press onwards. If it's too blurry then meter it in a slightly lighter place and go again.
Step 3: Long Exposures No.2
So now that we have an idea of how this works what can we do with it?
Well long exposure photography is an excellent way to show motion in photos or draw in them with a light source.
There are a few photos below that are fairly self explanatory after you read how to get them.
Ok so this is like the previous step in terms of setting except now we're playing with longer shutter speeds so drop the Iso by a few increments, say down to 100 or 200 iso, you might need to make the aperture smaller aswell if the shots are too blown out, experiment here, playing with the camera is the best way to learn.
For those without the luxuries of such creative control you'll be looking at using night mode outside or in a dark room, depending on how the camera feels like judging it you might need alot of light from your source.
The first photo was taken on a Canon Eos 400D, I know SLR but still possible with other ones, also I took these shots off my bebo page so quality is just okish...
The second photo was taken much the same way all 3s exposure and lots of moving...
Step 4: A Final Word on Long Exposures
Well this one is more for those with creative controls on their cameras, using the shutter priority function of your camera can be very interesting as well.
Check out how far you can go with this, at 15s exposure that's the maximum my fuji could do, this was one of the first photos I took with it, I was playing with the settings and had little to no idea what the photo would look like.
In the case of daytime or in this case simulated sunlight it can be better to let the camera do the smart stuff and give yourself only one control, by allowing the camera to figure out what it wants for the shutter time given you get to do the fun stuff.
Step 5: Time We Went Faster
So you're ready to try taking photos of really fast stuff now...
Definitely a moment to consider a few things, can you focus before shooting, ie: does the camera lens whir and the picture becomes sharper when you push the button half way in? If so you're able to do this in a quick and easy way, you need to focus on where the object will be (distance wise) and either follow and wait or wait for the object to hit the sweet spot. Settings wise you'll be looking at 1/2000th of a second at 200-400iso for a sunny day, again shutter priority is probably the best setting, I have found that full manual means that blown out pictures are too easy on a bright day.
For those without manual settings go for either full auto or one of the 'bright day' settings, they all have silly names but there should be one or two that have that general gist. Now if you focus beforehand then work away, this'll be easier with more light as the camera will lower shutter speed until it's happy. The actual shooting is the same for you guys just focus and wait...
For those with fixed focus you probably have a big enough depth of field to just shoot until you get a shot you like.
Step 6: So Playing With Focus...
Ok you're actually playing with depth of field, this is the amount of distance covered by that certain focus setting, remember old camera used to have a focus thing on the lens that had settings for so many meters up until the infinity focus... Well as you can imagine they had these because they only had a certain depth of field for each focus setting, though alot of digital cameras have a large depth of field due to their smaller apertures.
You'll notice in macro mode you get a very low depth of field, as little as a few centimetres sometimes.
You can use depth of field to your advantage and use it to give distinct foregrounds and backgrounds, take a look at the photo below, the bottle was out of focus because the camera was focused on the background while the much closer bottle was beyond the depth of field. I think that explains how this works much more simply than attempting to write it down.
For thse of you with fixed focus this is still do-able you just have less ranges of depth of field to play with, if you have a macro focus aswell it does give you the choice of foreground or background though. This exact shot is possible with a fixed focus because the bottle would be too close for the standard focus to have in sharp focus.
Step 7: Macros!
So you want to take close up photos of small objects? You'll need macro focus for that, plain and simple, but there are ways to get macro focus.
The rules change a bit here, you can quite easily have too much light, your depth of field is miniscule and you can't move the camera too much, or else...
So let's go on, in general the advice is take macros with the flash off but there's no complete rule, you should try a photo with the flash on, the one of the lighter below looked far better with the flash on, also due to the depth of field and a white background it has the effect of the lighter fading away.
Focusing. It's harder to get the autofocus to work on macros, you need a nice reference point like a pattern or some straight edges, just something that makes it easier to get a good focus on the item, failing that just go manual.
Shooting. You need to stay pretty still here, at maybe 1/80th of a second motion blur can occur but you only really need to worry at 1/50th and above. something like a gorillapod is a good idea now as they are a tripod but are very easily used for macro due to their flexibility.
Step 8: Learning More
The best way to learn, as mentioned earlier is to play with the camera, if you have a notion for a nice shot, take it.
Playing with techniques and experimenting with them is one of the best ways to figure out both your camera and how to take photos you really enjoy taking and like the results of.