Eli Bendersky has an outstanding post on multiple dispatch in Common Lisp. It’s part of a series he’s doing on multiple dispatch in various languages.
Lisp has always looked at OOP differently from most languages and Lispers consider CLOS a superior way of doing things. One of the ways it shines is in multiple dispatch. With CLOS, multiple dispatch is just a natural outcome of the way dispatch works.
The post is an excellent overview of CLOS in general. If you want to know what OOP looks like in Lisp, be sure to take a look at Bendersky’s post. In Lisp, OOP is easy and natural and works well in those cases where OOP makes sense. Even if, like me, you generally don’t care for OOP, you may find that CLOS will change your mind. On the other hand, as Paul Graham says, Lisp is the language where OOP is least necessary.