Common LISP is the primary dialect of LISP currently in use, and is used by most of the LISP community. The standard reference for Common LISP is a book by Steele. The Common LISP standard has changed slightly since the latest edition of this book. Information on the most recent changes should have come with your Common LISP implementation.
Unfortunately, the Steele book is almost impossible for a beginner to read. Good textbooks on Common LISP include:
Common LISP implementations are available from a variety of vendors, both commercial and non-commercial. The most popular commercial implementation for Unix workstations is produced by Franz Inc..