The jack has two terminals: a signal terminal that goes to the tip of a plug and a shield terminal that goes to the grounded plug housing and the cable shield. The signal terminal is usually a metal tab connected to the body of the jack with a small hole in it. Some jacks may have two signal tabs. If the jack is a mono jack, then you may connect the signal to either one of these. The shield terminal is usually a long strip of metal that may have a folded tab that forms a "pocket" for connecting the ground wires, or there may be a small hole in the bottom of the strip. The figure above is of the pocket variety.
If you plan to do a lot of soldering, it's worth investing in a good iron, as well as a good set of strippers and wire cutters. I use a temperature controlled iron set at 700 degrees with a chisel tip. This transfers a lot of heat quickly and melts the solder fast, which I prefer. There are a number of good Instructables on how to solder.
Before you connect the wire leads to the terminals of the jack, you should "tin" the wires by applying a small amount of solder to the wires. I use a cheap "helping hand" tool with alligator clips to hold my work while I solder.
After you've tinned the wires, put a small blob of solder in the "pocket" of the lead terminal. You should touch the soldering iron to the inside of the pocket to heat it up and then slowly feed the solder into the point where the tip of the iron and the pocket terminal meet.
Now we're ready to connect the wires. Fit the angled end of the signal wire through the hole in the signal terminal and solder it into place with a small amount of solder. Next, slide the ground wire up into the pocket and solder it into place. Use flush wire cutters to cut the wire ends off flush with the terminals. Using pliers, crimp the tabs on the end of the ground terminal to grab the cable housing. When you're done, it should look like this:
Note that there is little excess solder and there is clean separation between the signal and ground connections. It's worth taking your time to get a clean result.
Here's an example of a plug that has a small hole instead of a pocket for the ground wire. To connect the ground wire, simply bend it down to fit through the hole. Note that a large bundle of wire won't typically fit through the hole. To get a smaller bundle snip of half of the shield wire before you twist the shield to the ground lead wire.