My favorite thing to do with a 10 gal is to divide it. That way you can have double the bettas.
I use the double-divider method and have a buffer zone in the middle with the filter and heater.
For the frog-specific care you should check out the ADF care thread in the Compatibility section. Mike is right, whether or not you can have tank mates with your betta depends on his aggressiveness. Snails and shrimp are a good way to test his aggressiveness.
A fishless cycle will be best and will be shorter and better than subjecting your fish to that. If you know someone with a healthy fish tank, you can take some substrate and filter material from that tank to jump-start your cycle. It will significantly reduce the length of your cycle.