To work with copper you'll need the right tools.
1. a copper tube cutter
2. emory cloth
3. a wire fitting brush (make sure to get the right size for the pipe you are using)
4. flux and an applicator brush
6. a mapp gas torch kit, including a torch head and canister of mapp gas
7. an old rag
Here's how to do it:
1. Clean the copper. Cut the desired length of pipe and clean both ends with the emory cloth, at least as far up as the fitting will reach. Also clean the insides of the fitting with the wire brush.
2. Flux the joints. Flux is an acid paste that sucks the melted solder into the joint between the copper pipe and the fitting. Soldering will not work otherwise. When you flux a joint, flux both the inside of the fitting as well as the end of the pipe before putting them together.
3. Turn on the torch and get to soldering. First, make sure the joint itself is not touching anything, like papers that could catch fire, for example. Unroll the solder at least seven inches from the roll, and form it into a hook shape. This makes it easier to manage. Put the flame under the fitting joint, with the tip of the blue flame core touching the copper.
As the copper heats up, tap the tip of the solder to the top of the fluxed joint. It's not hot enough until the melted solder slips around and into the joint. When this starts to happen, remove the flame and rub the solder back and forth over the joint until it starts to drip out of the bottom. The drip may be overkill, but at least you know the joint is solid. If the solder doesn't flow easily into the joint, you may need to flux a little more.
4. For a little extra security, you might rub a brush full of flux over the hot joint. When it has cooled a little, wipe the joint with a wet rag. This removes excess flux from the copper, which would otherwise corode the metal. It seems silly to mention, but DON'T TOUCH THE COPPER RIGHT AFTER SOLDERING. It is very hot and will burn the heck out of you.
Soldering is a kind of art. Some plumbers don't care what their joints look like, only that they don't leak. Others make their copper joints look like they came out of a factory. The point, however, is that they don't leak. And, with a little practice, it's not that hard to have both.