If it's line of sight, then a simple way would be to use an IR transmitter and IR detector. The transmitter can be an IR LED pulsed at the receivers frequency (use a microcontroller, 555 timer, PWM IC, etc for this) this will create a logic high at the receiver output which can be used to trigger your circuit.
The transmitting driver can be something like below, using an NPN transistor driven from your PWM source (note that this example shows 36kHz, the receiver below uses 38kHz - the principle is exactly the same):
At the receiver you can see how it turns into a logic high (the bottom waveform):
Here is an example of a 950nm IR LED, and a 38kHz IR receiver. TO produce a logic high at the receiver, you send a stream of pulses at 38kHz with ~50% duty cycle.
Here is a PIC based IR remote project.
Simple but reasonable CD4017 based circuit.
Not a great circuit, but very simple. May be informative to play around with.
You may want consider buying a module like this one that can be used to control quite a hefty load (up to 12VDC/10A or 240VAC/5A)
Some more reading:
Remote Basics (images above from here)
Adafruit on IR sensors
You say you have some walls in between the sender/receiver, so an RF solution is they way to go in this case. Since it's just an on/off signal that needs to be transmitted, we can use very simple OOK/ASK Rx/Tx modules like this one:
The above is just an example, it basically just outputs at the Tx what goes in to the data pin on the Rx. There are many more on eBay if you search for "RF module", of varying types. Also places like Farnell, Mouser, Digikey sell various modules (purchasing from one of these is preferable for more complex modules as they are of a certain quality and come with a datasheet)