I'm not sure that would be a good project to learn to solder on, but it looks like you would be able to do it.
squirrel dog is correct, you will need a small soldering iron, something at or under 30 watts with a fine tip.
Wire- if you don't have any get a small role of 30 ga wire-wrap wire from Radio Shack.
It looks like all of the places you need to solder to are vias(holes through the board) with the possible exception of the yellow and green arrows.
Note, I havn't done one of these mods on the PS.
Strip the wire about a 1/4 of an inch. Get an old rag and dampen it in water(I normally use a sponge for this). Let the solder iron heat up and wipe it quickly on the rag. Take a small amount of solder and apply it to the tip(you just want the tip shiny, not a big glob on it)
Apply the tip to the hole. You need to be careful not to overheat the board, it should just take about 5 seconds or so for the solder on the board to "melt". Take the wire and shove it through the hole and hole it steady for a few seconds until the solder firms back again. Check the board closely to make sure that the solder has not bridged to anything else. Turn the board over and clip off any excess wire that came through.
Instead of pushing the wire through you can just solder it to the top of the board. Strip less insulation off of the end of the board, just enough to bend and fit on the solder pad. Heat the wire and put a little solder on it. Then like above, heat the pad till the solder melts and then place the end of the wire on the pad. The solder should cover the wire, remove the soldering iron and hold the wire steady until the solder firms up.
It's easier then I made it sound.
I love to learn by example.
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