All good points brought up so far...Also, what size tank is he in? Bettas in bowls often seem lethargic since they have nowhere, really, to swim. I have bettas in 5 gallon tanks and they are always moving around. One of my bettas right now is in some medicine in a one gallon bowl with a little Hydor bowl heater. The med helped, so I'll be transferring him back to the tank today, but in the bowl, he often did lie at the bottom.
You mention you just got the betta yesterday. Bettas often take a few days to get used to their surroundings. Don't be too worried that he didn't eat yet. Keep trying to feed him and get him used to the food that you have for him. The bettas that I get are all fed blackworms at the store, and it takes them a few days to get used to the betta pellets and freeze-dried bloodworms that I have for them. One of my new bettas didn't eat for 7 days. Hopefully yours won't take that long, but don't be worried if it takes him a few days to begin eating. He will take in the food and then maybe spit it out as he gets used to it. Soon he will eat it.