Fortunately Sidewinders are some of the easiest pads to hack because they actually come with little holes you can stick some 22 gauge wire into on the board itself. Alright, this better be a Gamepad sidewinder, otherwise this won't work, and you might also have to wire all the grounds seperately if its USB, I'm not sure, BUT if its a gamepad one, after you unscrew the back and pop it off, look at the PCB board.
Look in the bottom left corner and you'll see a bunch of holes that have letters by them, I believe the letters are "A, B, C, X, Y, Z, L, R, SH, ST" and I believe there's also a MODE and a GND one, but you don't want to mess with those. the L and R might be something else, but you'll figure it out. Now you're going to be getting your one ground point from the d-pad's contact point as it's easiest to wire to, so just worry bout all the non-common points for the buttons for now.
-Advice on soldering: first Tin the wire by putting a small bit of solder on the wire before you solder it to anything, so it basically turns the color of the solder. This is easily done by placing the Soldering Gun on the top of the wire, and putting the solder on the bottom, so when it heats up, the solder will flow up the wire, and cover the whole thing smoothly, just DON'T touch the wire too closely, I've burned myself many times doing that. Wiring to those small holes shouldn't be too hard with 22 gauge as long as you have steady hands. I've done tighter jobs with thicker wire, crappy solder, and my WAY overpowered soldering gun.
-The D-pads aren't too hard to solder too, check out my tutorial, it's not completely done, but it shows what you do to solder to the gamepad. The things I left out where that you have to tin your wire, heat up your wire prior to placing it on the game pad, make sure the soldering gun is nice and hot with a dab of solder, and DONT move the wire as it cools for about 30 seconds or so.
http://members.fortunecity.com/cthulhuluke/solder2.html if you need any more help, just ask
-Luke