First of all, you gotta understand the need of Windows Server 2008. To upgrade from Windows Server 2003 to Windows Server 2008, you must read the following article.
If you meet the requirement to upgrade to Windows Server 2008, you may proceed to upgrade it as step below.
1. Insert Windows Server 2008 CD.
2. Select Setup.exe to run it.
3. The wizard will should go through the upgrade. (If you have error, properly you may need to run in compatible mode)
If you have the compatible issue, you may go through the step as below.
1. Select Start button, point to Accessories, and then click Program Compatibility Wizard.
2. In the wizard, click Next.
3. Choose “I want to use the program in the CD-ROM drive” and click Next to proceed.
4. Choose “Do not apply a compatibility mode” and click Next.
5. Click Next again.
6. Check the box before “Allow non-administrators to run this program” and click Next.
7. Click Next.
Now you can double-click the executable file to upgrade Windows Server 2003 again.