I'm no expert, but I strip about an inch off the wires and push them together end-to-end. Then heat the wires (not the solder) by applying the iron to the opposite side of the wires the solder is touching, so as to draw the solder though the wires. Oh, and put the heat shrink over one of the wires before soldering them together. You can use a match on the heat shrink, if you're careful, but I prefer a heat gun. Use a rosin-core solder. The acid-core type makes a more brittle joint, I'm told.
Strip the ends of the wires.
Use fine sand paper, emery cloth or steel wool to clean any corrosion or coating off the wires.
If using shrink tube to cover the connection slide it down one of the wires now.
Twist the wires together making a good mechanical connection.
When hot, wipe the soldering iron/gun tip clean with damp sponge or rag.
Apply a very very small amount of solder to the tip of the iron/gun, just enough so it has a shinny coating. This is called tinning.
Heat the joint.
When hot apply rosin core solder to the opposite side.
As soon as the solder flows filling the joint remove the heat and solder.
Try not to move the wires till the solder has hardened. Usually a couple of seconds.
You should have a nice bright shinny joint and good electrical connection.
If using shrink tube slide it over the joint and heat.
If the joint is going to be exposed (out in the open uncovered), you can use steel wool or solvent to clean of the excess rosin. Then put on a light coat of clear lacquer. This will prevent oxidation and keep it nice and shiny.
If you are soldering a number of wires, when the iron/gun tip gets dirty or has burned rosin on it, clean and re-tin the tip.
Hmm, remembering my 2M class instructor berating me for sloppy soldering.
Acid core flux is for structural soldering (think slot car chassis) 60/40 rosin core is for electronics (but you should, best case, clean it with alcohol afterwards)
Stripping 1" of wire is too much. A centimeter or 3/8's is enough.
A helping hand is best, two alligator clips on pivoting arms with a weighted base to position the work precisely.
Pauls72 has it right but I will add that tinning the wires you want to solder helps too. Touch the iron to the tip of the wire and add solder to the wire when it melts. The trick is to do it QUICK and prevent any damage to the insulation. Oxygen is our enemy which results in corrosion.
Rosin core solder works the best for electrical work and is the easiest to use compared to having to brush flux on the joint and then use solid core solder.
When I'm doing large wire termination I strip the insulation off to where the wire is close to extending past the tubes end on the crimped on connector and then crimping the connection solidly onto the wire. This leave less voids that have to be filled with solder. Some people fill the terminal end with solder, tin the wire end and then with the terminal end hot and the solder in a liquid state shove the wire into the terminal. This works but I prefer having the least amount of solder on a joint but still have it work.
While I don't have any pictures of a cold solder joint these will exhibit a build up of the solder on top of the wires and terminal and the solder does not flow into the joint. Look at some solder joints on a circuit board and you can see how the solder flows and is smooth and flowing and that is what you want also.
Below is a shot of a soldered on terminal end on some 4 gauge wire. To heat the joint I know that a small solder pen or gun will not heat the joint up properly so I have to use a Mapp gas torch to get it to solder properly. You also have to watch that you do not use too much heat to destroy things like lifting the traces off of a circuit board. The discoloration (brown material) is nothing more than the left over flux from the flux core wire and if it is a joint you will see you can remove this material fairly easily by chipping it off. If you ever do circuit board soldering with joints close to each other and the junctions are on different circuits you need to chip this residue off and inspect the joint to where you can be sure you haven't jumpered it with solder when it's not suppose to be that way.