BASICS:
5 gallon tank minimum . Many hex tanks come in this size if that's the style you like, so that should be no trouble. This size tank will definitely fit into a small space like a worktop, desk, small table ect. There is no reason to get anything smaller ( which would be harder to maintain anyway )
Heater 26-28 degrees C.
Filter . YES they do need one. They are anabantids the same as Gouramis and need a filter just like they do. Most bettas prefer slow current or none, so a sponge filter is a good option to use. CYCLE the filter ( check out the fishless cycling thread in the new to the forum section )
EXTRAS/DECOR:
Silk or live plants You will need more than just a couple, bettas like lots of vegetation so get several bunches.
Gravel or sand substrate will be needed for live plants, if you go with silk plants then you can have either of those, or mny people use those decorative glass pebbles, and some people have no substrate at all and go with a bare glass base for easy cleaning.
Hiding places. A smooth hollow ornament is fine, some people like coconut caves, some people have even used a clean coffee mug!
Wood.If you decide to add any, make sure it is very smooth so the betta does not catch and tear it's fins on the wood.
MAINTENENCE:
25-50% water changes ( preferably 50% ) every single week. Make sure you use dechlorinator to treat the water you put back in. Regular monthly filter maintenence, and get a liquid test kit to keep an eye on your water parameters.
Basically it's the same as setting up any other basic tropical fish tank. Just with slower current, slightly higher temperature and no sharp decor.