Actually, you don't really need a PIC for something like this.
1. Just on On/Off switch.
Transmitter: Pulse an IR led at some frequency (say 40kHz). Make it so it pulses when you press a button on your remote.
Receiver: Receive the signal from an IR sensor (photodiode or phototransistor), put a bandpass filter with center frequency at 40kHz. Connect its output to a logic level converter (a simple transistor could work here). Then, connect the output of the converter to a JK FlipFlop IC. Connect J and K to Vcc and apply the output of the converter to Clock.
Connect your LED (with a resistor) to the output (either Q or /Q) of the FlipFlop.
They sell those IR receiver modules that receive the signal, amplify it, filter it and shape it to logic levels. If you use one of those, then connect its output to FlipFlop directly.
2. If you want to dim the light, then you should use the same transmitter. The receiver will have an Up/Down 4bit counter IC and a 4bit DAC IC (digital to analog converter), or you can use a R2R ladder instead of the DAC. IR Module's output will connect to Counter's clock, and its outputs to DAC's inputs. The output of DAC will go to the LED. Also, use an NAND gate IC (with 4 inputs) and connect it to the Clock of the JK FlipFlop (with J and K connected to VCC). The output of the FlipFlop will go to Up/Down selector pin of the counter.
In this configuration, when you press the button and hold it, the LED will start dimming. Then, if you keep pressing it, the LED will start lighting up again, then it'll dim, and so on.
In the second case, maybe you could use a PIC, but I think that it's much better to use several ICs, because you'll learn ALOT from that.
Good Luck,
TI|CP