both computers would need to be running Windows 7.
This WILL NOT stop you from having a home network however and thus sharing printers and drives. Both computers will simply need to be in the same WORKGROUP (and in both Vista and Windows 7 that is the default name of the workgroup). You will also need to have the same user account with the same password on both machines.
Here is a link that gives details and even offers a little movie about networking different versions of Windows:
http://windows.microsoft.com/en-US/windows7/Networking-home-computers-running-different-versions-of-Windows
Here is another helpful link:
http://windows.microsoft.com/en-US/windows-vista/Setting-up-a-home-network
Can I connect my two computers to a homegroup network? I keep seeing that you have to be running 7 to have network. Can you tell me how? I'm an older adult that went back to college and hate being stuck at the desktop to do schoolwork and would like to share my printer. Please help.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic