Rigging is the process of building a skeleton and attaching it to objects or an object, using figure mode.
I use two different ways
1) Each bone has an object attached, the bone influences all the vertexes in the object. I think the simple walk Robin tutorial uses this method, it works well for stick figures.
2) A single object. Each bone has an "influence" on each vertex/point. Check out the manual section figure-->Skinning
You could break your object up in point edit mode, then in edit mode, build ->split solids, copy and paste a part to a new object.
Or you could keep one object and use skinning to assign the bone influences. This takes some practise. I prefer painted weights. I recommend experimenting with a single cylinder with two bones. You can change the strength of the painted weight brush in build -> weight brush. Change it to 1 and it will be more obvious what is happening. In the pic the blue bone influences the blue parts of the object, the red bone influences the red part of the object. Notice I am in flat shaded view so I can see the vertexes I am painting. Switch to sequence mode and test - it is easy to have influences that are only seen when the bones are moving.