hi :D, i will try my best to cover all the information (other members please correct me and add anything on :D)
The tank needs to be at least 2.5 gallons, the bigger though the betta, i would really invest in a 2.5 - 5 gallon aquarium which has everything in it.
a heater is a must as betta's like warm temperatures 78 degrees and above (not to high though) so it the water has to be at least 78 degrees and the heater will make sure there are no fluctuations in the water which can harm your betta.
A lid for a betta is a good idea, as betta's have been known to jump out of there tanks, so again if you can find a nice size tank, it should come with a lid.
You can have a filter and it helps to keep the water clean, however the current cant be to strong as betta's don't like strong currents. Even if you have a filter you still need to be doing 25%- 50% water changes weekly, if you are going with a 2.5 gallon tank then i would recommend a turkey baster (to suck up uneaten food etc from the gravel). also use water conditioner when adding any water to the bowl/tank as it takes out the harmful chemicals in the water (you can get this at any petshop selling fish and fish supplies)
There is one member here who keeps her two betta's in bowls (separate bowls as bettas shouldn't be mixed as they can harm each other), and they use a filter and a heater, and both bowls look just as nice as a tank.
Betta's can be feed betta's pellets, and tropical fish flakes (some betta's don't take to the flakes though), live/frozen food can be given but some live/frozen foods (for example blood worms) can cause a betta to bloat.
If you want to keep live plants, it helps to have a florescent light (usually comes with a tank that has a filter, heater etc with it), and you also have to make sure that the plants are fully aquatic, as plants that cant be fully submerged can eventually rot and cause you water quality to fluctuate. It is a misconception that the betta will eat the roots of a plant and you don't need to feed it, it will eventually kill your betta, so i don't advise you do this.
The best plants would be something like java moss which doesn't need high lighting and can be tied with nylon thread to decorations, also try and avoid floating plants that cover a lot of the surface area at the top (e.g duckweed) as betta's have an organ which enables them to breath oxygen from the surface.
Other things you would need is a fish net, liquid test kits (to test the water parameters e.g ammonia, ph, nitrates and nitrites), turkey baster or syphon tube (cleans the gravel).
Also read the betta FAQ in this forum :
here is the link
it will cover anything i've missed and most probably give better information lol :D