There are two main ways to sew with interfacing, either by pressing it on with fusible interfacing or by sewing it in wtih sew-in interfacing. I'll go over both.
There are tons of different weights of interfacing, differing on what kind of fabric they should be used with and for what type of projects. Basically, the rule is this: heavy fabric = heavy/thick interfacing. Lightweight fabric = light/thin interfacing. The only exception would be if you need something to have a lot of reinforcement. For example, I've made princess hats for my neices that used a thin, satin-like material, but needed a heavy interfacing to support the "cone" shape.
In doing some research on this, I also found an awesome use for interfacing: you can iron it to your sewing patterns to extend the life of the pattern. I actually found this tip, and even a few tutorials, in various places on the web. But it looks pretty straight forward. Basically, use a pressing cloth (to protect the paper pattern from scorching) and iron on a light weight fusible interfacing to your pieces. SUCH a great idea.