All the procedures and fees are here:
www.cic.gc.caThe time depends on which country you apply from. You can find out average application times at the same website.
If you move to a different country in the middle of your application, there are a few things that could happen. If you maintained an address in the UK to receive and respond to mail, then everything would be pretty easy. But if you change your address with CIC in the middle of the application, you risk that some of your mail will go to the old address. You could also have someone be your representative, in which case you would use their address throughout the whole process. This is what happens when you hire a lawyer.
Anyway, start by reading the website. Good luck.