It might also be worth reading the How do we introduce undergraduates to digital humanities thread.
One of the difficulties is that digital humanities covers such a wide range of knowledge and skills that you'd really need to narrow things down to choose an entry point. For example, I came into DH via educational technology, so my starting point was in tool building and site building. For that, I good entry point was just to install WordPress, Omeka, and Drupal someplace and build a site, maybe hack on the themes and code.
As Scott mentioned, there is also a lot of GIS work being done. Not knowing much about GIS, I'm not sure what a suitable entry point is (though I guess that finding an ArcGIS tutorial or class would be a start).
Same with things like distant reading or text-mining or data visualization.
That's all completely unhelpful, I know. Maybe an alternate step back is to lurk and listen to the online conversations that touch on digital humanities until a topic comes up that sounds interesting, and try to ask about the details in that conversation?