I recommend you to pass by this article, and this Chris Coyer article too. And of course, this one that had a great impact on the web. SitePoint has a complete guide about this topic. And here is a demo, just in case. Let me know if it helped.
Had a look, but the content in my cells goes (has to go) across multiple lines, and all these solutions are made for simple data. Might go for a simple scrollbar for now and see if I can come up with an elegant solution :) Thanks for the links though!