1) If you haven't already done so, open your Everleap account. Use your current domain name. you'll be testing your site on Everleap with a Secondary URL. Pointing your domain to your Everleap site is the last step of the moving process.
2) Download a copy of your site and database from the current host.
3) You'll find your Everleap FTP configuration information in Control Panel. Add your new Everleap site information to your favorite FTP program.
4) Upload your site files to the /wwwroot directory in your Everleap account.
5) Click the Databases link in the Control Panel navigation and set up your MS SQL or MySQL database.
6) Attach or restore the copy of the database that you took from the existing site. For MS SQL you can do that here, for MySQL, here.
7) Update the database connection string in your application. You can find the configuration info in Control Panel: MS SQL, MySQL.
8) Now you can browse your newly uploaded site using the Secondary URL in Control Panel, and make any necessary changes or adjustments.
9) If you are moving your email to Everleap as well, you can enable email service and set up your users now.
10) If your database contains visitor generated data you will have to shut down or disable any parts of the application that make database entries at the old host before you make the final name server changes. That is necessary to prevent users from making "orphaned" entries into the database at the old host.
11) After you have shut down the application at the old host you can make a final copy of the database and attach or restore it to the new database in your Everleap account.
12) Once you have attached or restored the final version of the database you can change the name servers for your domain to point to Everleap. DNS updates take anywhere from a few minutes to 24 hours, depending on your ISP. It's best to leave your site up and running at your old host for a day or two after you've completed your move if possible. That way visitors whose DNS doesn't update quickly will still see the site on the old server, even though some parts of the application may be disabled.