Hmm, perhaps someone else on this forum will be more familiar with those chips, but I can't say I know much about them or used anything similar, so I can't comment too much on that.
A couple thoughts, though:
-On the transmitter circuit, that LED is connected directly across the 5V. Without a resistor to limit the current, it will probably burn out pretty much immediately if it is a standard LED.
-The eBay description of the receiver says that it requires a 50 Ohm, quarter wavelength antenna. Do you have that?
If you have an oscilloscope, you might try looking at the data input of the transmitter to determine if the chip is sending whatever data it is you are inputting. If no data is being sent by the chip, then the issue may be with the way you have the 2262 chip configured. If you are seeing data going into the input of the transmitter, then check the data output of the receiver. Is it receiving the data being sent? If not, there may be some issue with the RF transmitter or the RF receiver. Unless you have a very high frequency oscilloscope or other more specialized RF equipment, you probably won't be able to look at the radio signals directly, so you will probably have to consult whatever documentation came with those transmitter/receiver boards. The receiver appears to have a trimmer capacitor that may require adjustment for it to work properly. If there is data coming from the receiver board, then there could be some issue with your 2272 chip configuration.
Whatever YouTube videos or web pages you looked at might have more information if you are having issues using those 2262 and 2272 chips. If you would like to link them here, it may help us get up to speed on how you are using these chips and help debug whatever problem you are having.
Personally, this does not really strike me as an easy project for a beginner. Unless you copy everything the person in the video did perfectly on the first try, then debugging a circuit like this is not a trivial task. RF circuits are even more complex, especially in the hundreds of MHz like this, so we are basically going on blind faith that those modules you bought on eBay are working correctly.
Edit: I have attached the datasheets for those two chips for reference.