Soldering is a process of bonding objects together (usually metal on metal) with a soft metal called solder. You can find solder at stained glass stores, and it comes in different kinds of metal including tin-lead, tin-zinc, lead-silver, cadmium-silver, zinc-aluminum, and tin-silver and tin-bismuth. Each solder type has a specific use. You probably would not want to use lead based solder in your jewelry, but the tin-silver may work alright if your metal jewelry isn't heavy. That kind of solder is usually used for electronics but it may work with what you're doing. Here's a link with more information on tin-silver solder: http://www.azom.com/Details.asp?ArticleID=2377
There are some other items you need for soldering items together. You can find all of these at your local stained glass shop. The first, is a soldering iron. You need to make sure that the iron has a temperature that reaches or exceeds the melting point of the solder you're going to use. Then you need a liquid called flux. Flux gets brushed onto the place where your solder will attach your pieces together. It prevents oxidation of the metals (caused by the high temperatures used while soldering) and it reduces the surface tension that occurs when the super hot solder comes into contact with the cooler metals you're attaching together.
The last item you may want is an oxidizing agent. It's another liquid that gets brushed onto your piece and makes your sodder look aged. If you go to a stained glass shop, take your jewelry pieces with you and the store clerk should be able to help you pick out the correct supplies for you!
Beyond that, what you need to do with your supplies is simple on paper, but slightly difficult in application, so I suggest you practice a couple of times before going to finish a jewelry piece. Another note: this is based off of my experience with stained glass and i know that there are certain metals such as silver where you can just heat up the area that needs to be soldered and it works- but I haven't had the opportunity to try that out, if anyone has the tutorial for that way of soldering?
Soldering based off of Stained glass soldering:
1. Make sure your metal pieces to solder are clean and free of debris.
2. Make sure you're in a well ventillated area on an uncluttered fireproof work surface that has access to an outlet for your soldering iron, turn on your iron and let it heat up.
3. Layer your metal pieces and decide which points you're going to solder.
4. Brush some flux onto those chosen points.
5. Take the solder and unwind it a little bit and straighten it out- do not clip from main body of the solder.
6. Take the soldering iron in your better hand and lower it to about an inch above your metal pieces.
7. Bring the solder in to touch the tip of the iron, after a second or two the solder should melt and form a bubble on the iron tip.
8. Take the main body of the solder away from the tip of the iron, and lightly touch the tip of the iron to the fluxed area on your piece. The solder should slide off the iron's tip and onto the metal pieces. The tip to soldering is having the eye to not add too little or too much solder to the joint you're soldering. It simply takes time and practice to do this.
9. After soldering all the different points, turn the iron off and let the piece cool down. You can use this time to clean up the area.
10. After the piece is cooled, clean it off with soap and water thoroughly, making sure the flux is completely cleaned off.
11. If you're using an oxidation agent, use a brush to dab it onto the solder joint and wait for the recommended time on the package before washing it off and giving your piece it's last cleaning!