In both cases, you need to launch a Clojure subprocess. This is most commonly done using a tool such as Leiningen.
SLIME and Swank Clojure
Once Leiningen is installed, run
lein plugin install swank-clojure 1.3.4
M-x clojure-jack-in once Leiningen is installed to begin a Slime session for the current project.