Moving a site from one URL to another


I have two questions.

#1. Whats the easiest way to move one wordpress site from one URL to another? What are the pitfalls and the things that I should look out for? How will this affect my SEO if I would to do that? What if any drawbacks, etc.

#2. The next thing is how can I move the same wordpress site with the same URL onto another webhosting service? I have someone hosting in Godaddy and I would like to move his site for him onto my hosting. Any thing I should look out for when I move his wordpress site?