It’s going to be much easier to do this using the traces on the back of the controller… you can’t really use the front because you need the rubber pads (that press the buttons) to be unobstructed.
The image below shows where the traces for each button is (A-green, B-Red, Y-Yellow, X-Blue).
To solder to these you will have to use something small and sharp (I use a needle) and lightly scrape the green off until you’ve exposed the copper inside the trace.
You can usually solder to the copper fairly easily.
Be careful that you’re only exposing the copper under the light green color (the line running from the hole). The dark green on the outside of the trace is grounded, you don’t want to expose that before soldering.
After you’ve exposed something to solder to for each button you can follow the instructions Toodles gave you above.
The small points of solder labeled on the pic above show where you’ll solder to LB and LT.
You can buy diodes at Radioshack.
Here is a graphic to explain what he means when he talks about each end of the diode.
Also, someone else will have to confirm this, but I believe at the end you will have to cut the traces that run from LB and LT, so that those don’t trigger their original functions.
Hopefully someone with more experience can confirm this.
Let us know if this is at least a good start to helping you with the project, and we can respond to any questions you have about doing it.