Along with the fairly standard soldering iron, a new jack, and such, there's a few other things you'll need. You'll need a box cutter or X-Acto knife to score the outer cable before using a cable stripper to remove the outer covering. You'll also need a microtorch, and a hot glue gun. some people also like to have a little paper or electrical tape, but in my case, i've chosen not to use it. You'd also note two different styles of 3.5mm TRS Jacks- You only need one - the plastic sort is cheaper and looks more 'original', but i prefer the metal one- i've had the plastic ones fall apart post soldering at least once, despite being internally very similar.
Helping hands also are useful - jacks are tiny and need clamping.