The other two posters are correct in that you can most likely simply move the drive from one machine to another.
However, if you have two computers, you can benefit in the long run by having them networked. For one, you can share an Internet connection. Assuming they are reasonably close in proximity, get a 4-port ethernet switch (around $40) and 2 Cat 5E patch cords of the appropriate length. If you connect to the Internet via a dedicated router, you can point both machines to it to automatically determine network settings. Otherwise, you can set up your network manually by giving each machine what is called an IP address (use one that is dedicated to private network use, such as anything starting with 192.168).
It's beyond the scope of this forum to explain exactly how to configure the network, but you can access and change that information on the Windows box with Settings->Control Panel->Network Connections, and on the Mac with System Preferences->Network.
There is a ton in infomation on the web about how to network computers for home use.
Good luck,
Michael