Soldering is basically the joining of metals by a fusion of alloys, which have relatively low melting points. Soldering is a must have skill in electronics. It is also a skill that must be taught correctly and developed with practice.
Equipment
You'll need a soldering iron, solder, and a wet sponge. Irons of the 15W to 30W range are good for most electronics/printed circuit board work. Using anything higher in wattage will risk damage to the component or the pc board. Using the correct type of solder is also important. Use a thin rosin core solder.
For solder to properly adhere to a connection, the metals must be clean and free of all nonmetallic matter. You can clean a dirty lug or component with a small steel-bristle brush designed for the purpose, you can also use a solvent such as alcohol.
Now, to solder the connection. The idea is to apply the tip to the connection and almost simultaneously apply the solder to the junction between the tip and the connection. You want a small amount of solder to flow between the iron tip and the wire or component, which aids in transferring heat to the connections. The connection becomes hot enough for the solder to flow onto it, forming a solder fillet between all the parts.
Keep the soldering iron against the connection long enough to "cook out" any flux residue, but not so long that the solder "burns up." The time for the entire operation should be very short, just a matter of seconds. Don't let the solder run down the tip, or try to heat up the whole area first. Apply just enough solder to fill the gaps, and no more. Why? Excess solder will flow into places where it is not needed, or where it can cause a short.
To complete the process, remove the solder first, then the tip, being careful not to allow the connection to move while the solder is solidifying.
How Good Soldering Looks
A good connection is one where the solder has uniformly flowed over all the surfaces to be connected, following their contours. The connection appears bright, shiny, and smooth, with all wires in it appearing well soldered. However, if the connection is rough, grainy, or flaky looking, or if the solder formed into little round blobs, or has ridges or sharp points, redo it. Take the time to visually check the connection with those points in mind.
If the joint is a "cold" connection, caused either by insufficient heat, a wire moving, or foreign matter(such as oxides) getting into the connection, the cure is simple and direct: re-heat the joint and apply a little more solder. If that would place too much solder in the joint, you will have to remove the solder before trying again.