It is recommended you start the process at least a few days before the time runs out on the account with your present host. This will keep your website from experiencing any downtime between the moves.
The first thing to do, after you have searched and found a new web hosts, is create a backup of your website. Make a new folder somewhere on your computer. Using your favourite FTP program, such as WS_FTP or Cute FTP (these and other FTP programs can be obtained at download.com), download all the files and folders on your website to the new folder you just made on your computer while maintaining the same folder and file structure (this will be important when uploading your files and folders onto your new host’s server later). Make a note of any special CHMOD permissions you have set on any file or folder (look in your FTP program’s help documents for information on checking a folder or file’s CHMOD permissions). You will need to reset the permissions after you upload your files and folders to your new web host’s server.
If you have any scripts or programs that you made a database for, make a backup of each database. If you have a database...