I know that "asdf" is a packaging system. I don't remember reading reading anywhere that it's a requirement but a quick grep through the slime directory shows several references to "asdf".
the copy of asdf that i've been using has some fixes for openmcl and can be found here: http://evins.net/downloads/asdf.lisp
the minimum you'll need is for asdf to be located somewhere in your *module-search-path*, so that (require :asdf) will find and load it. my openmcl-init.lisp looks like this:
(pushnew #4p"home:lib;openmcl;" *module-search-path* :test #'equal) (require :asdf)
there's a good asdf and asdf-install tutorial here: http://weitz.de/asdf-install/
you may also want to look at my require replacement for openmcl that will integrate with asdf: http://sexp.typepad.com/sexp/2004/02/require.html
if you have further openmcl-specific problems getting slime running, you can contact me off-list or find me on #lisp.
...bryan