This is my second basic soldering guide from the beginner, for the beginner.
It covers soldering and unsoldering the most basic component, a jumper wire.
Never soldered before? Start with Soldering 101: Tin the Tip.

If you appreciate this instructible, please visit my blog for more ideas:
GoodCleanCrazy

You will need:
All the items used in Soldering 101
flux paste
insulated jumper wire
pc prototyping board, veroboard (stripboard), or padboard.
wire strippers
dikes (diagonal cutters) or flush cutters.
solder sucker (desoldering pump)

**The links above are simply the place I found these items. Any suggestions for other US links would be appreciated**

Step 1: Strip the Wire

Open the strippers. Poke about half an inch of wire in a cutting groove slightly smaller than the wire diameter. Clamp the stripper closed and rotate it about a bit. Then flip the stripper over and pull the wire through.

Step 2: Tin the Wire

Twist the end of the wire to clean it up a bit.

Dip the end of the wire in flux.

Then stick the wire in something to hold it still. I used a pair of pliers.

Tin the tip of the soldering iron.

Imediately after tinning, hold your iron and solder on opposite sides of the wire. It is important that you hold everything very steady until the solder begins to flow. As soon as solder flows, quickly move the solder and iron out to the end of the wire. This should quickly coat all the metal with a thin layer of solder.

In a perfect world, Terry (my soldering overseer) says the iron should touch the wire a fraction of a second before the solder does. And of course, remove the solder a fraction of a second before removing the iron.

Move too slow and you get melted insulation, which doesn't actually hurt anything, but wouldn't pass a NASA inspection apparently. You could also get large globs of solder on the wire.

Step 3: Solder the Jumper to the Board.

Poke your tinned jumper end through your PC board.

Clean and tin the iron tip.

Again, hold the iron on the opposite side of the wire as the solder. Briefly touch both iron and solder to the base of the wire.

A good solder joint is shiny. If yours is foggy or dull-looking, you've got what's called a cold solder joint. This is bad. It's weak and has poor electrical connectivity. Either your iron wasn't hot enough, or you need to clean the tip, or you took too long to solder that sucker. Try melting down the existing solder again.

The solder joint should also not have too much solder. A little volcano-shaped hill all around the base of your wire is a nice "fillet" joint. A bulging, rounded hill is bad, as is a spot around the base with no solder.

Step 4: Clip the Excess

Set your cutters very close the base of the wire.

Flip the board over and cup your hand underneath. This keeps you from getting large eye-surgery bills.

Cut the excess wire off.

You're done soldering!

Step 5: Desoldering the Joint

In this final step of the exercise, we'll desolder the jumper.

Turn up the heat all the way on your soldering iron. The quicker we can do this, the better, and heat helps.
Also, taking too long can cause the copper pads to separate from the board and even burn the board.

Clean and tin the iron tip.

If you've never used a solder sucker before, just play with it--you'll figure it out in two seconds.

Holding the solder sucker tip very close to the solder, melt the solder and quickly suck up the solder.

You should now be able to easily pull the wire free.

Alternatives to a solder sucker include solder wick (hold the wick between the iron and the solder until it flows into the wick) and just heating up the solder and pulling on the wire simultaneously.

I much prefer the sucker for speed and ease.

That's about it. Don't forget to clean and tin the tip of your soldering iron before putting it away, and happy soldering!