You have two initial options, doing a backup and restore within MOSS to move the data, or doing it at the SQL/STSADM level. I prefer the latter, as it isn't nearly as inclined to fail and leaves you with more flexibility.
1) Find the content Database,
These are listed under Central Admin->Application Management->Site Collection List
2) Backup the content database,
You could alternatively detach it, and copy it. Just doing a backup in SQL Server Management studio is easier.
3) Restore content database to new server
Copy the BAK file to new server. Create an empty DB in Management Studio, restore from backup, you may need to change an option in the "options" tab of the restore dialog to get it to work. (Overwrite db).
4) Create Web App on new Server
Central Admin->Application Management->Create or extend Web App->Create New Web App.
5) Associate restored DB with new Web App
Central Admin->Application Management->
SharePoint Web Application Management->Content Databases->
Remove Content Database from your new web app.
Now use STSADM to add restored DB to this web app
c:\program files\common files\microsoft shared\web server extentions\12\bin on new server is where you can find the STSADM.
run this command from there.
stsadm -o addcontentdb -url http://yourwebapp:port -databasename yourcontentdb -databaseserver yoursqlserver
6) Run ISSRESET from command prompt
* Make sure your running the same service pack level on both source and destination sharepoint if possible.
* Make sure you install all webparts, solutions, features, etc on new server before you restore the content database, so that it can find all the features it's looking for
* Leave your old site and contentDB intact until you get the backup running on the new server, this way your ok if there is a problem
* DON'T try this with your config database! It won't work