HowTo: Run Node.js on Heroku
It's not hard, in principle: there's a buildpack for that, or rather for running Node.js apps on Heroku in particular: and it's open-source, and theoretically pretty simple.
The documentation is a little spare, though. In particular, it assumes that you've already created a build server on Heroku and made it available to buildpack scripts.
If you haven't, or if you just want a little more hand-holding through the process, check out this longer tutorial from Pat Patterson.
Here's a completely unofficial, unsupported recipe for running your own Node.js version on Heroku. These instructions are based on those at the Heroku Node.js Buildpack repository, with some extra steps that I found were necessary to make the process work. Note that buildpack support at Heroku is still evolving and the process will likely change over time.
Pat's recipe also includes helpful notes on which warning messages can be ignored.