Just to add my $0.02:
A few years ago, learning to use a darkroom would have been more-or-less essential for anybody on a career path in photography. With so much commercial photography today going digital, though, I'm not sure that's true any more. (But then again, I'm not a professional photographer, so I could be misinterpreting that world from my outside view.) That said, having the experience and skillset to use a wet darkroom certainly won't work against you if you want to pursue a career in photography, and could conceivably open some doors. OTOH, time spent learning these skills could conceivably be spent learning other skills. With the digital world so much in flux, though, I'm not sure how much you learn today (on Photoshop, say) would be applicable in 5-10 years. So there's my wiffle-waffle response.
As to how to start out, I recommend you read some Web sites and/or books on traditional darkroom work. One Web site I have bookmarked is
this one, which has good basic information on most of the procedures involved, as well as tips on constructing a darkroom. I've also found Tom Grimm's
The Basic Darkroom Book, 3rd Edition to be a good printed guide. As others have noted, you can get by at first with remarkably little. On the other end of the scale, if you get into it in a big way you might eventually spend thousands of dollars constructing your ideal darkroom -- but presumably not at this stage in your life!
You might want to start with developing a few rolls of B&W film. You can then scan the film or take it to a 1-hour lab to have them make prints. (You might get back hideously colored prints, but at least you'll be able to judge the images pretty well.) Developing the film only requires a room that can be made completely dark or a changing bag to load the reel and put it in the tank. The rest can be done at any convenient sink. Once you've done a few rolls of film, if you're still interested, set up the enlarger in some location that can be made light-tight and start printing. If you're still interested after doing that for a while, you can improve your darkroom space, add color processing to your repertoire, start toning your prints, and otherwise expand and improve your skill set.