How big

How big of a tank should you have before you start adding other fish in the same tank as a betta?

10 gallons IMO.
Anything less is a bit small even for the betta itself, you start adding other fish and it's going to be cramped. Smaller tanks also don't support much of a bioload.

Hi there,
theres no real concrete answer to this question, as bettas are tempermental fish that run the gambit from peaceful and non-aggressive, to super aggressive almost murderous personalities.

Some bettas will not tolerate any tankmates, others are content in a community tank.

Now if the betta is in a small 1-3 gallon tank, theres no room for any tankmates.
In a 5 gallon tank, you could try an apple snail, or maybe a bamboo shrimp or other large (bigger than 2 inches) type of shrimp. Small shrimps may be eaten.
Another option would be a trio of white cloud mountain minnows (3).

In a 10g tank, you could easily have room for more fish - a school of neon tetras (6), or a school of a smaller variety of cory catfish(5-6) for the bottom, etc.

If you really want to have a community tank, with lots of room for each fish, and to allow for space if your betta turns out to be one of the more aggressive individuals, a 20 gallon tank or larger would be your best bet. This would allow for space, good water conditions, and allow you to add more than just a couple more fish.

What size is your current tank?

Thanks Sneaky! You always have very good and detailed info. I currently have my betta in a 1 gallon tank. I know! I know! I am planning on getting a larger tank for him. I am interested in learning more and eventually have a real nice community tank, so your response was great.

Nevada