Use Save Bodies to save each of the bodies in your part out as individual parts. You have the choice when you do that to automatically create an assembly. You can Fix the parts that you know are in the correct locations. You can add Concentric mates to the parts that you want to pivot about the skinny cylinder. After that you may have to use some of the more esoteric mates depending on exactly how you want things to move.
If you want to model some of the parts as a subassembly and you want the parts to move relative to one another when in the main assembly, then you want that subassembly to be flexible. You do that by setting the properties of the subassembly.
It might help to go through a couple of the tutorial example in Solidworks.
- Lesson 2: Assemblies - A basic intro to assemblies
- Assembly Mates - A more in depth task of assembling a machine
The second one in particular is good for understanding the concept of how individual parts are assembled into a machine.
After that you should have a good idea of how to approach the task.