There are a few options.
First one is easy: Heroku. They have a free tier that is ample for deployment and testing. I won't go into further detail on this, but I decided not to use Heroku anymore.
Another common option is Amazon AWS. I gather most apps on AWS use lein-beanstalk [sorry, no citation here]. Lein-beanstalk has been out for quite a while and appears to be well-maintained. It is also maintained by the same person who maintains Compojure.
I use a VPS. I set up the linux build with Nginx and deploy with git. So, basically, my flow is create the site, compile to lein uberjar, then deploy. I know that some people can and do use the leiningen "lien ring server" cantation on their apps and use many other configurations, such as Maven, Tomcat, deployment with Vagrant, etc, but I just run java -jar myApp-xxxxx on the server and it works great.
As far as documentation, there does appear to be a dearth of documentation on Clojure deployment specifically. Sort of have to bang your head against the wall and figure it out if you want to go the VPS route the first time you do it. I found that almost none of my issues involved Clojure specifically.