They need very clean water to grow well, so good filtration and frequent water changes are necessary. Also a heater, of course. The babies I bought from a breeder LOVE their grindal worms, which can be fed starting at about a month old. Cultures are available on eBay and they are super low maintenance. You can also buy frozen brine shrimp and daphnia at your local pet store and they like those a lot too. Babies can't swallow normal sized betta pellets, so you'll need to crush them or buy pellets that are pre-crushed or smaller specifically for them to eat.
I have had a disaster with a heavy fake plant falling on top of a baby and killing her, so definitely make sure any decor is stable. Babies love to hang out in plants.
Depending on the size of your tank and the baby's age, you may want to only keep it half or 3/4 of the way full so the baby doesn't have to work too hard to reach the surface. By 2 months this isn't a concern and you want to make sure your fishie gets lots of exercise :)