Step 1: Find the Electronics
Make sure you have plenty of light to work. This modification requires only a few soldering joints (as few as two) but one of them can be pretty difficult to do, so be sure you can see what you're doing.
Remove the transparent plastic that protects the circuitry; it can go back on later.
Step 2: Find the Test Point
Now, look at all those gold-colored dots on the circuit board. Those are test points that can be used by technicians to access various functions of the hardware to test it. Note the small wire going to the touchpad button -- that also leads to a test point and eventually to the microcontroller. The button shorts to ground when pressed.
If you have a voltmeter you can verify this by setting it to continuity check and touching the trackpad's chassis and any of the 4 small contacts on the button; two of the wires will "beep" always, the other two only when the button is pushed.
Near the main chip, look for 4 test points placed like the arrow keys on a keyboard. You want the "right arrow" in my picture. Pulling that to ground marks a secondary click (aka right click) event to the microcontroller, which dutifully reports it to the rest of the laptop.
Step 3: Find the Test Point for the Primary Button (optional)
Step 4: Get the Right Sort of Wire
With a soldering iron, let the wire end "soak" some solder in, then cut the tinned (soaked) part until only a bit is visible from the insulation; this should help prevent shorts. About six inches of wire is more than enough.
Step 5: Solder the Wire on the PCB
put a little bit of solder on the iron.
"poke" the test point so that some solder remains on it.
hold your wire end against the test point.
poke them again with the iron so that the solder melts together. Keep it there for about half a second.
This is critical and it's also the only time where you can break something, so be sure to have plenty of light and be calm :) I recommend holding the soldering iron vertical. Use the thinnest tip you got.
Step 6: Connect, or Make, a Pushbutton
Step 7: Fix Your Switch in Place
When you push the corner of the button, the (metallic and grounded) back of the button will touch the wire you added.
You're done! All you need to do is close it up.
Step 8: Close It All Up!
Put the piece of transparent plastic that protects the electronics back in place, use another layer of tape to hold it there if you have to.
Note that on my particular laptop I didn't even need to open it up... (Well, on MY particular laptop I had to because while I was at it I also cleaned the fans).
Video of it working (in case embed acts up) : http://www.youtube.com/watch?v=PPjDi4E_c3A
If you like my work, check out my autonomous robotics page at http://www.robotseverywhere.net/