How Do I find what my operating system is in my computer?

Choose About this Mac from the Apple menu.

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Your question is a Mac 101 so as a follow through to Niel's post I would recommend you stop down to your local book store and peruse the many books on the Mac and Snow Leopard. Check out books written by NY Times Tech contributor David Pogue. He is informative and his style is geared toward basic learning.

Following Niel's and sig's suggestions and assuming that you're new to Macs, but know windoze boxes, see these:

Switching from Windows to Mac OS X,
Basic Tutorials on using a Mac,
Mac 101: Mac Essentials,
Mac OS X keyboard shortcuts,
Anatomy of a Mac,
MacTips, and
Switching to the Mac: The Missing Manual, Snow Leopard Edition.

Additionally, *Texas Mac Man* recommends:

Quick Assist,
Welcome to the Switch To A Mac Guides,
Take Control E-books, and
A guide for switching to a Mac.