Common Lisp comes in many different flavors, or implementations. Two popular ones are Steel Bank Common Lisp (SBCL) and Clozure Common Lisp (CCL).
If you're a newbie to Lisp, it might be easiest to pick one of the two implementations above and get started, without worrying too much about which implementation is best for you. However, there are a lot of implementations that all have their pros and cons. For a complete list, see Wikipedia's big list of CL implementations.
A good way to get started with Lisp is to go through Practical Common Lisp book.
Also, you may want check out Articulate Lisp site for getting started on Common Lisp ecosystem.
This is a JSCL Lisp REPL running on the Web. Note that it is not a complete Common Lisp implementation, but enough to have a taste of it: