This is meant to be a checklist of things to do when you change hosts. I just did, for the first time in about 10 years! Went fairly well, but the first item is based on a mistake I made--fortunately the site was offline only from late Saturday until about half an hour ago, not a big deal.
1) Upload your files into the correct location (if you don't, your site will not appear when you do item 2)
2) Change the nameservers for your domain name. Your new host should give you instructions and the new nameserver names.
3) Set up email addresses related to the domain, if any. Make sure that you set them up as they were previously.
4) Set up an error page for "file not found" situations. This is a simple page that tells people what has happened and should have links to your home page and main site sections. Your host probably has a generic one--you want to set up one that is specific to your site.
And now I get to two things I haven't yet done:
5) Set up redirects from "yoursite.com" to "www.yoursite.com" and vice versa, as well as "www.yoursite.com" to "www.yoursite.com/index.html" or whatever. I'm a bit vague on this and would appreciate advice. I know the idea is to make sure that all incoming traffic is funneled in the same direction...