Well, it's pretty straight forward but it's not quite as easy as a newcomer would think...
First step is deciding on your led color. This is important to know what color the led is because this very loosely determines what is known as the 'forward drop voltage'. This voltage is what actually helps you calculate the correct resistor value to use.
lets say you want to install one single blue led and you want it to be very bright. I would first look on the led's packaging to find the forward voltage. if non is found I would google "blue led forward voltage" and come up with a typical figure of 3.3v.
I would then read the led's packaging for the highest current value (mA) that the led is rated for. if non is found assume it is 20mA.
Now find an led resistor calculator online somewhere and punch in your desired values. The gameboy's positive rail is at 5v.
So with a power supply of 5v
and a drop voltage of 3.3v
and a desired current of 20mA
we get a 100Ω resistor for one blue led.
If you want multiple leds you should wire them in parallel. This means that both positive pins are soldered to a positive rail and both ground leads are soldered to ground. 'Daisy chaining' these leds does not work like you would think it does.
I hope my explanation wasn't to convoluted