A DNS Flush might speed things up if your ISP DNS has picked up the change. You can test if you are on the new server by going to a fake URL on the site (just make up a filename) and if you get a grey bar along the top with red error text, then you are on the new site.
The move involved:
- Getting hold of a new server
- Install control panel software, MySQL, PHP etc...
- Freeze old database and make a "dump"
- FTP old files + DB dump to new server
- Restore DB dump to new database
- test, test, test
- Change nameservers from old host to new one
- Bingo!
Most of the time was spent adding lots of tweaks to PHP and MySQL to make sure that lots of things are cached.