There are a few steps you need to take to move your EVE Server to a different computer:
Click here to visit the downloads page and download the latest version of EVE Client and Server.
Click here for installation instructions including system requirements.
Click here for instructions on how to open up SQL Server so other computers can communicate with it on the network and for information on Firewall settings.
If you don't already have a database backup, click the EVE Globe icon at the top right of EVE and click Backup Now. You can do this in EVE on any computer connected to the old server but, regardless of which computer you use, the backup file will be created on the old server. EVE will tell you the location of the backup file when the backup is complete. It will have a .bak extension and will be called eve.bak or PCName_eve.bak where PCName is the name of your old server computer. But, if you have renamed the database in the past it will have a different name with the .bak extension.
Copy your most recent backup file into the folder called C:\EVE Backups on the new server. Start the EVE Database Utilities program and click OK on the Connect form.
Click Restore Database and then Apply
On the Restore DB form, use the values shown in the screenshot below but replace eve.bak with the name of your backup file if different. Click Restore Database. This will cause your database to be restored to the C:\EVEDB folder - i.e. after the restore you should see eve.mdf and eve.ldf in that folder.
Open EVE on each PC where you have it installed. At the Connect prompt, click Edit Settings. Change the Data Source entry to be the name of the new server computer with an \EVE suffix
If you followed the instructions above, the Database will be called eve but, if you called it something else, make sure you set the Database entry appropriately