Recreate all email address using your new control panel. If
you are not familiar with this your webhost should provide instructions
for doing this.
Make sure that all software your site uses is working properly.
Maybe you will have to change config files if database, username
or password are different from your old host. If something doesn't
work properly check the rights of your scripts.
Extensively check that everything is working. Visit the site
at your new host and test it carefully. As typing in your domain
name will take you to your old site you will have to use the
IP address your new host gave you: http://XXX.XX.XX.XX - if
your site will not have it's own IP address, you will have to
use something like http://XXX.XX.XX.XX/~username. Make sure
that all links work.
Change your domain record
The very last thing to do, is make sure you login to your registrar
and change your name servers. Within 72 hours, your website
will be working great