All you need is something to cook on, a way to get it to the site, and enough money to cover the entry fee and the meat (and fuel, beer, etc.) :-D
Seriously, I have seen one person teams up to teams with more people than I could count. Personally I think two people os the minimum, but there are a lot of folks who cook alone. You just have to be good at multitasking.
As far as equipment, you need to be able to cook at least one butt, one brisket, two or three slabs of ribs and 9 or more chicken thighs. hey are not all cooking at the same time, but you may have to juggle a bit to get everything done on time. Lots of teams cook with a couple of WSMs and do well. To me three WSMs is a good setup since you will probably want to cook a couple of butts and briskets and more ribs and chicken pieces to have more choice for turn in.
As far as money, there is an older thread on competition costs. If you factor in meat, rubs, sauces, fuel, entry fees, travel costs, etc., I think an average of $500 per competition, MOL, is a good starting point.
How to get started? i would suffest visiting a Brethren team at a comp local to you first, just to see if you are really interested. Then volunteer to help a team out so you can get a feel for the stuff that happens when the crowds aren't around (tending the pit in the middle of the night, etc.). I would also suggest becoming a CBJ and judging a few comps to get an idea of the turn ins and the quality of the food. Finally, jump on in! You can also look for backyard events near you (rib cookoffs, etc.) and try oneof those.