This is an overview of the basics for soldering wire. Includes tools, techniques and basic theory.
Solder is an alloy with a low melting point relative to common metals used as materials. It is used as a filler material to join such metals, as they would otherwise require much more heat to fuse. Wire soldering is a method for joining (splicing) two wires together using solder.
Step 1: Tools/Materials:
- Wire (copper, preferably stranded) 
- Wire strippers 
- Dikes (cutting pliers) that match the wire size 
- Heat shrink matching the wire size (generally 1.5X the diameter of wire) 
- Wire holder (optional) 
- Soldering iron, preferably temperature controlled (with a dial and display) and a sponge 
- Solder 40/60 rosin core (lead free if possible) 
- Heat gun 
- Safety glasses 
- Jeans (recommended) [not pictured]
Step 2: Before You Start:
Ensure that you are wearing safety glasses, molten solder can get flicked in the air. Jeans are recommended in case of drips. Tie back long hair and make sure you don’t have loose clothing.
CAUTION: Solder often contains lead. Avoid touching your body. Wash your hands well afterwards.
CAUTION: Do not breathe the smoke that comes from the soldering iron.
CAUTION: Soldering irons and molten solder can reach high temperatures. Do not touch these items while they are hot.
CAUTION: The heat gun looks like a hair dryer. It is not, it reaches very high temperatures and can burn you. Never point it at yourself or another person.
Step 3: Prepare the Workstation and Materials:
Plug in the soldering iron. If it is temperature controlled, set it to about 750-800°F. Add water to the sponge if it isn’t made of brass threads. If you do not have a sponge, use a wet paper towel in its place.
Cut wires to desired length with the dikes. Set any extra wire to the side.
Step 4: Strip the Wires:
Strip approximately three times the diameter of one end of each wire (stripping is removing the insulation from the wire to expose the copper strands) using wire strippers. A razor blade is often required to strip larger gauge wires.
Step 5: Prepare the Soldering Iron:
By now, the soldering iron should be heated up enough to work with. Break off about a 6” strand of solder. Feed some solder onto the tip of the iron and quickly wipe it off on the wet or brass sponge. The tip should now look silver and clean; try to keep it this way throughout the soldering process. A clean tip is a happy tip
Step 6: Tin the Wires:
Ensure that there are no stray strands of wire by gently twisting them all together if necessary.
Tin both wires by feeding a bead of solder onto the tip of the iron and touching it to the bottom of the exposed wire. Allow it to momentarily heat up, then feed solder into strands, allowing the stripped section to fill with solder.
The bead of solder placed on the tip of the iron prior to tinning is referred to as the "wet bridge" or "thermal bridge". The bridge allows for faster heat transfer by increasing the area of contact between the iron and wire.
Step 7: Cut and Place the Heat Shrink:
Cut a piece of heat shrink 1cm longer than the stripped wire that has the most exposed copper using dikes. This is to allow for 5mm of heat shrink on both sides of the splice.
Slide the heat shrink over one of the wires, past the tinned section.
If you are practicing, this can easily be done at a later step. However, it is good practice to do this before splicing wires, as it cannot be done so easily when the wires have connections at the other ends.
Step 8: Splice the Wires:
Place both wires end to end with their tinned ends overlapping.
Splice the wires by creating a wet bridge, then use it to push one of the tinned ends into the other. The tinned solder should quickly liquefy and join; lift the iron when this happens.
Let the splice cool for a few seconds, then tug on both wires to test it. It shouldn't break easily if the splice was done correctly.
Step 9: Apply the Heat Shrink:
Slide the heat shrink and center it over the splice. Use the heat gun to shrink it by moving the gun around the heat shrink to get an even distribution of heat.
Step 10: Clean-up:
Put away all of the tools, make sure to wait for the soldering iron and heat gun to cool down first.
Wash your hands (you don’t want to keep lead on you, especially when you eat).