Interesting...but so many ways to do this!
You could just use any remote control for a TV, DVD player, VCR etc. When you press any button, a serial bit-stream of infrared pulses is emitted. An infrared receiver (just three wires to hook up) will then give you a repeating digital code stream output whenever you push a button on the remote.
Now, you are faced with a lotta options.
The dirtiest way is to pull the infrared LED diode out of a discarded remote control to become an emitter, a source of invisible magic infrared light that only requires a 9-v battery to a button momentary contact switch and a current limiting resistor, approx. 50-ohms to the anode of the infrared diode , cathode of the diode returns to the neg term of the battery. Now you have the transmitter built.
For a receiver, you can buy an infrared phototransistor/photodiode or else you can again take one out of a discarded DVD player VCR. etc VCR's use two of them standing up next to where the VCR Cassette sits to detect when the tape has run out in either direction and there is also one in the front panel inside a small remote control receiver, easy to spot because of its lens peering out of a small metal case.
Now you hook the collector of the photo transistor/diode to +9V on the receiver, the emitter goes to the base of an amplifying transistor, emitter of the amplifying NPN transistor to ground through a 1K resistor. The collector of the amplifying NPN transistor connects to the cathode lead of the LED you want to light. The anode of the LED to +9V.
Now you cover the infrared phototransistor/photodiode receiver with the same visually opaque very dark infrared passing piece of very dark red plastic that you've taken off the discarded remote remote control to shield your receiver from room light and sunlight or else your receiver LED will be on all the time.
Now you just point your transmitter at the receiver and push the button!
A more difficult and challenging way to solve this problem and spending a few weeks to do it, is to take an infrared receiver out of a discarded remote controller device and feed the output of it at the emitting infrared LED's pin to your scope and record the waveform for any particular button pressed on the remote control of interest. Be careful, the transmitted code is modulating a 38KHz carrier to eliminate room light interference and narrow the bandwidth of the transmitted signal in this common remote xmit-receive scheme.
Another way to do this so that it only works with your custom secret remote control code is to modulate on and off the transmitting infrared diode with the output of a 555 timer at some fixed carrier frequency, say 38kHz. Then you can use an infrared remote receiver module to receive this secret code and feed it to MCU which can quickly determine the frequency and it then lights your LED. You then also simply press the remote button at a rapid pace to create low freq. code.