you can find your shell by typing
echo $SHELL, and it should return one of the following:
/bin/bash --> Bash Shell (also called Bourne Again Shell)
/bin/sh --> Bourne Shell
/bin/ksh --> Korn Shell
/bin/csh --> C-shell
/bin/tcsh --> Enhanced C-shell
Sometimes it might show as something like /usr/local/bin/bash but that would be the same shell that /bin/bash is (even though it's not in the same directory).
There are other shells such as the POSIX shell and whatnot but the ones I've listed are the most common types of shells out there.
If you are new to Linux/Unix and want to find out more I strongly recommend O'Reilly books, which you can find at most bookstores like Borders or Barnes & Nobles, or can find at their site
www.oreilly.com.