For the most part there aren't many tools required to build a computer.
Though while you are out buying parts you might want to pick up a good set of screw drivers from someplace like Best buy. You don't want to use a standard screw driver since most of them are magnetized.
Magnets and computers are never a good mix.
Something else to consider would be some kind of cable organizers. There are several options, from Zip ties to cable ties. These help keep your wires neat and untangled which will ensure they remain in good condition for a very long time.
Some kind of grounding strap, often times these will come with the screw driver kit. A grounding strap will ensure that you don't shock your computer parts with static.
With the parts and tools we can now prepare to build the computer.