Assuming I send a signal wirelessly to a receiver connected to a fan. if the receiver detects that a pulse is there, it switches on the fan. the fan should stay on until it detects another high pulse, then it should switch the fan off thereafter. How could I make this happen?
Maybe a D Flip Flop? Tie the /Q to D and then the clock becomes your input. Each pulse (rising edge) should toggle the Q output pin state. That pin can then control a relay/FET/whatever to gate your fan.
If you use a latching relay on the fan end, it can latch on a high pulse, then "un-latch" on the next high pulse. You will have to check the relay datasheet to be sure the length of the pulse is long enough to latch/unlatch, and that the voltage and current requirements are met for the relay coil latching.