1. Small cup - BAD. Even with 1 betta, you should give him at least 1 gallon of water. I keep mine in 2.5 gallon tanks.
2. Labyrinth fish. They breathe from the surface. Every so often you will see him take a breath. Therefore no need for surface agitation.
3. Filter - always good, but stick to the little ones you hook up to an air pump - Bettas' natural habitat is rice paddies. They like still water.
4. Temperature - they are hardy and can handle most any reasonable room temperature, but their natural habitat is THAILAND which is quite warm most of the year, if not downright hot during the summer. If you can keep them in a room that is at least 75F or a heater suitable for a very small tank to get the water to around 80F, they will be happier.
5. Mirrors/Other Bettas - believe it or not, bettas are healthier when living in the company of other bettas. Maybe it's competition? If you keep a 2 male bettas in a tank with a clear divider, they will be brighter, bigger, and build more bubble nests, which is a sign that they are happy and healthy. A little mirror in the tank isn't bad in a pinch.
6. Food - contrary to what the lady in the mall may say, you can't just let them eat the roots of a plant. They might survive, but how happy would you be if all you could eat was a root? Buy them floating betta food and also feed them brine shrimp or blood worms for a treat. Only feed them a little bit - 4-5 pellets.
7. Cover - They like cover. Put plants and furniture in the tank that they can hide in and swim among.
Feed daily, change the water weekly. Make sure you let the replacement water stand for a few hours to dissipate the chlorine and allow the temperatures to equalize. They can handle a wide range of temperatures, but rapid changes will kill them. Bettas CAN handle a 100% water change.
Have fun and don't get addicted. My ex-gf started breeding them. It was crazy.