I agree with turusan on soldering and brazing, but welding is joining two pieces together by melting both pieces. Usually there is a third metal that is heated as well to help with this process. Most welding I know and practice is either wire feed or stick welding. Wire feed is a machine that feeds a strand of wire charged with electricity and you have the pieces to be welded connected to the opposite charge of that electricity. When the wire hits the metal to be welded the current flows and melts everything together. Stick welding uses a rod (metal stick with flux on it) that you hold with a clamp and put against the metal to be welded. The same thing happens, the current causes everything to melt together.

Welding uses a torch to melt the pieces at the joint that you are fusing together (no external alloy or material added as a joining agent). Soldering uses a soldering iron (like a probe) and and a low-melting point alloy (called a solder) to join two pieces together. Brazing is a type of soldering, specifically using an alloy/solder of copper and zinc at high temperature, usually associated with joining pipes. And yes, solder is pronounced like "sodder" (the 'l' is silent).

I'm not sure, but I'm almost certain the first syllable of 'solder' is pronounced like 'aaa', and the 'L' is silent. The tool used for solder is called a 'soldering iron'. It is pronounced like the verb.