Now what you need to do first is plug the soldering iron in. Let it heat up, but please do not touch it. It causes some very nasty burns : ( I chose this iron since I had it around, but all you really need is a low power one, if I remember correctly mine was in the 15W range.
Also purchase some solder, very cheap at Radio Shack. Mine is the Rosin Core (used to do a lot of PSX mods : ), but others will work too. Now strip the wire on the molex and fan so it looks like this:
Now slip on a piece of heat shrink on the wire before soldering it together. Heat shrink provides the neat covering and shielding of the bare wires. You can also use electrical tape, but it might get messy. Take the iron and grab some solder and just touch it lightly onto the wire:
After dabbing that on, you should have something like this:
Sorry for the horrendous picture, somehow my hands shook while shooting this one but you get the idea. Now remember that heat shrink I told you to put on before? Take it and slide it down over the bare wires you just soldered:
They call it heat shrink for a reason, it shrinks when you apply some heat to it! Anyway, you can go the easy route and get a lighter and just burn it that way. But I prefer a cleaner and slower solution. Use a hair dryer:
I just walked into my bathroom and borrowed my housemates dryer. It provides enough heat to cause the plastic to shrink: