I'm a bit of a sumo fan, so perhaps I can add something here.

I remember seeing sumo on ESPN(2) not too long ago. If I'm not mistaken and we're talking about the same show, it was the September basho. I don't know what to say about scheduling. What I'd do at home on breaks is look in the TV paper for the week and see if it was on. It's almost always on ESPN or ESPN2 and in early evening, so you can just skim those two columns or rows in the listing each week. Not super convenient, but it works *if* the TV paper is right. There is a web site that posts Real Player videos of matches if people are interested. It may not be 100% complete, sometimes a day is missed or the guy doing it is away for a basho, but it's certainly more than you'd get by many other means. Go to
http://www.oz.net/~drc/sumomovies/movies.html to see what's currently available.
As far as rankings go, yes, there are probably web sites and FAQs that explain it better and/or in more detail, but it's almost exclusively a win/loss thing. Win more than you lose and you won't go down; it's not guaranteed that you'll go up, but it's rare that you won't. Lose more than you win and you won't go up; same guarantee bit. Sumo has a number of big divisions and the top one is what you usually see with a number of named rankings. Throughout all the lower levels, it's win/loss records that move you up or down. Once you make it into the highest division, Makuuchi or Makunouchi, things change a bit. The lowest rank within this division is Maegashira, up from that is Komusubi, then Sekiwake. Moving between these is again a win/loss thing. The level above Sekiwake is Ozeki (sometimes called "champion"). Getting that promotion is a different matter. The head organization has to decide whether or not to promote you based on things like consistently good winning records (like 10-5 or better repeatedly), staying in the hunt for the title during the second week, and winning against a Yokozuna (rank above Ozkei, the "grand champion" level) now and then. Once you've reached Ozeki, there's no automatic demotion for a losing record. Instead you get put on kadoban status, basically a warning. If you get a second losing record in a row, then you're demoted to Sekiwake. However, once demoted, if in that third consecutive basho you pick up at least 10 wins, you get waived back up to Ozeki. If not, you have to fight for it from scratch. As for reacing the Yokozuna rank, it is basically as Cthulu said. Again, the head organization has to make the promotion decision and they normally do look for two consecutive tournament wins as a minimum requirement. As far as I can remember, that's not actually a hard and fast rule written in stone that they *have* to follow, but it's sort of become an unwritten rule. I think it is possible to get promoted to Yokozuna without two consecutive yusho (tournament wins = Emperor's Cup), but it seems unlikely. I think there are some other factors involved in the decision, too. Since the Yokozuna are your grand champions, they have to be role models and demonstrate the very best of sumo. Search web sites for more on that if you're interested. Oh, and yeah, you have to be an Ozeki to get promoted to Yokozuna. Currently there are two Yokozuna, Musashimaru and Takanohana since the other recent one, Akebono, retired in January. If I'm not mistaken one rikishi was recently promoted to Ozeki, but if so I forget which one.
Wow, that was more than I probably thought I would write when I started, but I hope it's helpful.