If you are totally puzzled from your last host due to any of reason you can change your host for this first of all, it's very important to have a backup of your website and everything related to it, like databases, scripts etc. It will be very helpful in case there is data loss because of any unforeseen reason. Save at least 2 copies of everything and store them separately, so that you can work with one and the other one will function as a backup. You can take backup in various ways.
Once you have taken a new web-hosting plan and you are ready to upload your web pages, databases etc., check that you have received an IP number, FTP or FrontPage login, and password from your new hosting company. Now, upload all your files to the new server.
Before transferring your DNS servers over from your previous host to your new one, debug and test the new site from an individual IP number. Check that all the web pages exist, the links point to the right pages and that all your scripts are running.