Lisp (an acronym for List Processing) is a powerful programming language designed to create other computer programs. The most used form of Lisp today is Common Lisp, it's available on every computer platform and uniform in use through a standard reference manual.
To start programming with LISP you need to install an integrated development environment (IDE). The good news is that there are many Common Lisp IDE's available for free:
Allegro Common Lisp a free version is available for Linux, Windows, Mac OSX and FreeBSD
Armed Bear Common Lisp (ABCL) a free open source implementation for Linux, Windows, Mac OSX and FreeBSD. Needs to be compiled before installing so possibly not the best choice for beginners.
CLISP available for Linux, Max OS X, Windows, xBSD, Solaris, Tru64, Solaris, HP-UX, BeOS, NeXTStep, IRIX, AIX
Lispworks a full commercial version and a free 'personal edition' are available for Macintosh, Linux, Windows and FreeBSD.
SBCL Steel Bank Common Lisp, a free open source implementation available for Linux, OSX, FreeBSD and with a version 'in progress' for Windows.
There is also a very good Lisp plugin called CUSP available for the Eclipse programming environment.
Choose and install a Lisp IDE for you platform and follow these Lisp tutorials and exercises to start learning Common Lisp today.