Many misconceptions surround the temperament of the Siamese fighting fish -- more often called the betta. While these fish can act quite aggressively, this aggression is very selective, and in most cases they make fine tank mates for other species, including African dwarf frogs.
In general, bettas only fight with other bettas. In fact, only male bettas fight other male bettas for the most part. Female bettas will happily share a tank with other female bettas without incident. Males bettas will rarely bother female bettas, unless it's breeding season. In this case, males may chase and harass a female that is unwilling to breed. However, bettas of all sexes rarely bother other fish. The sole exception is that male bettas occasionally go after similar-looking aquarium fish, like long-finned guppies.
African Dwarf Frogs
Unlike bettas, African dwarf frogs don't have a single aggressive bone in their bodies. In fact, with African dwarf frogs, you only have to worry about picking tank mates that will not bother the frog or out-compete it for food. These frogs can comfortably live their entire lives underwater. One note of caution -- avoid purchasing the similar-looking African clawed frog. This species can grow to larger than eight inches and will readily eat most aquarium fish, including bettas.
Despite the fact that both bettas and African dwarf frogs are often kept in unheated bowls, both species really need real aquariums to thrive. For one, both bettas and African dwarf frogs come from the tropics and need warmer-than-room-temperature water to thrive. Additionally, both species benefit from full aquarium filters like most aquarium pets.
When selecting other tank mates for bettas and African dwarf frogs, you have several restrictions to worry about. First, you need to avoid any aggressive species, since both bettas and these frogs are not very aggressive toward other species and have trouble holding their own against more boisterous fish. You will also need to steer clear of fish with reputations as fin-nippers, since bettas' long, flowing fins make them irresistible targets. At the same time, you need to avoid fish with long, flowing fins like guppies, since these are some of the only fish to trigger bettas' aggression.