It is pretty simple to implement the RF control to the circuit, you just need to swap the push button for the RF module
There are several different modules, but the most common ones are those 4 channel modules.
The Arduino is linked to one of the channel pins (in our case, using the code of the 1st page, the Digital pin 2 of the Arduino will be linked to D0, D1, D2 or D3) in all cases you will still need a physical Pull-Down resistor or to use the built in Pull-UP activating it via code.
If you wanna see if the signal is being correctly received by the receiver, you can add a led on the VT pin, that will blink when the receiver is receiving any data.
as you guys can see, it is pretty simple.
There are several different modules, but the most common ones are those 4 channel modules.

The Arduino is linked to one of the channel pins (in our case, using the code of the 1st page, the Digital pin 2 of the Arduino will be linked to D0, D1, D2 or D3) in all cases you will still need a physical Pull-Down resistor or to use the built in Pull-UP activating it via code.
If you wanna see if the signal is being correctly received by the receiver, you can add a led on the VT pin, that will blink when the receiver is receiving any data.

as you guys can see, it is pretty simple.