I have read that it is good to have several libraries in aperture 3 rather than saving all photos to one library.
Where did you read that? I recommend the opposite.
If I have say 10 libraries from 10 different shoots
Aperture works very well with "one Project = one shoot". This is one of the basic design paradigms, and should be followed unless you have a good alternative plan.
Do they all save to the one vault or do I set up 10 and name them all differently (the same as the library presumably)? As I back up do they all find the right library?
The User Manual chapter on Backing Up covers this. Each Library has it's own Vault. You _must_ manually create and fill the Vault. You name each whatever you would like (the Vault is a Finder file package). Common practice is to store your Vault(s) on a second, usually external and moved off-site, drive.