It's pretty easy to get a Clojure web application up and running on Heroku. Heroku's Dev Center has a good Getting Started with Clojure article that shows you how to install the Heroku client and get your ssh keys setup. It has a very basic "Hello World!" Ring application as the example but you'll probably want something a bit meatier to play with. Here's how to get the FW/1 for Clojure example application running on Heroku...
Follow that Getting Started guide to get Heroku setup but when you get to the "Write Your App" section, do the following:
git clone git://github.com/seancorfield/fw1-clj.git cd fw1-clj heroku create --stack cedar git push heroku master
You should see several screens of output flash past as Heroku downloads all the dependencies needed to build and run a FW/1 application and then you should see something like this at the end:
-----> Discovering process types Procfile declares types -> web -----> Compiled slug size is 11.3MB -----> Launching... done, v4 http://some-domain-1234.herokuapp.com deployed to Heroku
Go to that URL in your browser and you should see the User Manager example application! (some-domain-1234 will be whatever domain Heroku has allocated for your web application)
After that, just edit your application, commit it, and push it up to Heroku. Heroku will update the dependencies if necessary and redeploy your application. It's that simple!