If you have the receiver that goes with it, perhaps you can reuse it.
I am not very familiar with RC transmitters, but on a cursory search it appears 2.4 GHz transmitters don't use any standard protocol, nor could I find any datasheet for this particular unit. As such, if you don't have the receiver, you'll have to reverse-engineer the protocol.
While this is technically possible, it's not easy. You'll need significant expertise in radio engineering and a lot of time. It's not something that could be covered within the scope of a single Stack Exchange answer. If you wanted to go down this route for educational or entertainment purposes, I'd suggest gaining some familiarity implementing receivers for protocols that don't require reverse engineering first. With the ubiquity of wireless electronics you probably already have at your disposal many devices that transmit some standardized, documented wireless protocol.
Furthermore it's not really worth the effort. For just a few dollars you can buy all kinds of transceivers which would be easy to interface with a microcontroller and which come with a datasheet so you don't need to reverse-engineer how they work. You would certainly spend more than the cost of a pair of such devices just on the equipment you'd need to reverse engineer your RC transmitter.