The procedure differs depending on whether you are using slime-connect to start slime (by connect to a remote swank server, created with lein swank, for example) or you are starting slime using M-X slime.
If you're using slime-connect, you'll need to modify the classpath of the java process that is running the swank server. If you're starting the swank server using lein swank, simply add the jars you want to be part of your classpath to the project's lib directory.
On the other hand, if you're starting slime using M-X slime, the following elisp code will do the magic for you (just place it in your ~/.emacs file).
(eval-after-load "swank-clojure"
'(progn
(add-to-list 'swank-clojure-classpath
"/Users/smcho/.clojure/")
(add-to-list 'swank-clojure-classpath
"/Users/smcho/.clojure/blah.jar")))
This will add /Users/smcho/.clojure/ and /Users/smcho/.clojure/blah.jar to the classpath. (Please note that you'll either need to restart emacs or reload the .emacs file: type M-X load-library and then type .emacs on the next prompt.)