A 5 gallon tank works fine. Please no one keep a Betta in anything smaller than that. Personally, though, I would probably get a 10 gallon, so I don't run out of room to add plenty of Cories or Otos, and maybe a snail. Also I think it would be much easier to maintain a 10g.
Of course that's for a male Betta, or a single female. I'm not sure if I would put three females (they have to be kept in three's or more, no pairs or they will fight) in a 10 gallon or not. I'd be a little worried they would be too crowded, then again it might work just fine. I might go with a 15g minimum for females, then there'd be room for a few other fish.
I am planning to get 3 or 4 female Bettas for my 20 gallon Long.
Okay, I have to weigh in here. I know more than one person who has gotten say a betta bowl or one of those 2.5 gallon small tanks for one, and they do okay in those. They can live a good deal of their lifespan in such a container.
Having said that, 5-10 g is good in order to have a betta that is as much fun to own as can be, a betta that is more responsive, active and happy. The contrast between bettas in small containers and ones in 5-10g containers is astonishing; they go from quiet rather sleepy fish to curious active fish that explore all the time that they are awake.
I have to agree with poefox, they are much more active and entertaining in a larger tank. Mine was in a small 2 1/2 gallon tank temporarily until I got the 10 gallon. In the smaller tank he mostly just slept. Now he's constantly active and exploring. Bettas seem to be very curious fish and love having "toys" in their tank to play with. In a small tank it's just not possible to create a good playground for them. They get bored very easily...