I recently had to move my hosting from one company to another. Even after working with websites for over a decade, and transferring hundreds of sites before... when it was my own sites, I dreaded the process. My personal site, for example, had over six years of posts and photos of the kids. I certainly didn't want to lose that! Here are some tips I can give you for transferring your website.
- Backup Everything - Obviously you're going to download everything from your current hosting... but make sure that it really is everything. If your site is backed by a database (WordPress, Joomla, phpBB, etc) you're going also need to backup the database. Also, depending on how your website's e-mail is setup, you may need to back that up too.
- Pay Double - Don't try to end your hosting on one day and start your new hosting on the next. I recommend overlapping for a month. You can have everything setup at the new place and simply change the DNS. If all is working fine, you can cancel your old hosting. If something goes wrong, you still have the old site waiting, to temporarily go back to, or to help you troubleshoot what's wrong with the new one.
- Don't Panic - When you transfer your site and it doesn't work, don't panic. It's usually something very simple. Make sure there wasn't a default index you needed to delete. Check that files that need to be writable are CHMODed correctly. If you had modified your .htaccess, make sure you re-modify your new one, a lot of FTP programs hide this file and it may not have gotten transfered.
- Walk Away - If all else fails, walk away from it. Often what is an obviously mistake can be impossible to spot if you've been looking at it to long. Go AFK, relax for 15 mins, and come back. The problem might jump right out at you!