There have been several threads since the first wii modchips so I suggest you go for them.
Quicksolder is "feature" that allows you to dribble solder between the chip PCB and the mainboard. Personally I hate the concept and suggest you use wires instead (ironically some quicksolder guides suggest using uninsulated wire to help).
Materials:
Soldering iron, as fine a point as you can get. There is some debate over the wattage. I plump for a 30W personally but I have been doing it for years, others go lower towards 15W.
Solder: Depending on where you are in the world lead is apparently evil so new lead replacement solders are appearing. The only nice commercially available in replacement in my opinion is the CASTIN series but a trip to your small holder store should yield some lead tin solder.
Flux: some swear by it but I do not see the need. The solder should come with it and whatever you do make sure it is not a nasty flux designed for industry/automotive sector.
Screwdriver: Phillips and Triwing (common name for the three flanged screws set 120 degrees apart from each other). I make mine but they should be able to be obtained from the same place you get your chip or a quick search away.
Wire: wire in the US tends to use American Wire Gauge aka AWG to measure thickness while most others use millimetres. Larger AWG values correspond to thinner wire with most going for 30AWG or 0.225 mm wire. There is a trade name called kynar which refers to the sheath (nice because it is hard to melt with an iron).
Practice, you probably have some old electrical junk around, this is as good as any. I was trying to find a picture but the points could easily be contained within the smallest coin you have (and you need multiple wires in there).
A light and magnifying tool may not go amiss either. A desoldering wick or a solder remover/sucker may also be a wise investment.
How easy to mess it up? I would say the risk is not bad but people never cease to amaze me on this one. If you have a new Wii (assuming it is not a D2C one) then chipping with cut legs becomes much harder, some dremel down while others attempt to make connections with the small ends exposed.
Good luck.