has some decent info but I disagree with some things and it's not my favorite betta website. I recommend the following sites:
Some of them are probably better for breeding but they still have nice info
As far as your questions...
* How big should the tank be?
1-gallon is the bare minimum...I highly recommend getting an aquarium at least 2 gallons. The 2.5 gallon Mini-Bow kits are pretty popular and not very expensive but don't use the filter that comes with it...it's too strong and can damage their fins. In a tank less then 5 gallons you don't need a filter anyways.
* I had a beta when i was little but i can't remember what we fed it, what do you feed yours?
I rotate between HBH Betta Bites and Hikari Betta Bio-Gold. I definately recommend both =). The bettas in my community aquariums sometimes snack on Omega One Fish Flakes but most bettas don't like flakes so I'd stick to pellets. It's also a good idea to supplement with frozen foods such as bloodworms and brine shrimp. Freeze dried foods, on the other hand, are not very healthy and should only be given as a treat. Remember that it's normal for your new betta to not eat for a few days...or even a week! Don't worry, he won't starve.
* Should he have any thing special in his tank, little fisherman, etc.?
I would get some silk plants (plastic can rip their fins) and a place to hide such as a castle or hidey rock. If you want to do live plants then I'd recommend anacharis for a small tank. Java fern would work, too, but you can't plant it...it should be tied to a rock or piece of driftwood.
* How often should his tank be cleaned out and given fresh water?
That depends on what size tank you get. A 2-gallon aquarium should be cleaned out completely every other week and on the week you don't do a 100% water change you might want to do a partial water change and maybe clean the gravel. Always remember to decholorinate your water.