How to Transfer WP Blog to a New Web Hosting Provider?

I’m moving my website and my WP blog to a new web hosting provider. I understand that first I need to backup my blog database and blog files. But what do I do after backing up the blog? Could anybody tell me all the steps required to complete the transaction smoothly please? Thank you very much in advance!

P.S. I’m using Yahoo hosting now, but want to try a new one. If anyone who has transfered their blog from Yahoo to someone else before could share their experience, that would be great.