I don't know why, but I like these plans better:

http://www.unlimiteddimension.net/Dprops/trapplans/trapplans.html

Your materials will depend on what you are working with.

Your most important tools are things you cannot buy:
Patience
Elbow Grease
Gumption
Common Sense

What your tangible tools will be will depend on what materials you are working with. As mentioned above, power tools and hard wood will give you the best results, but if you're careful, one could make a nice trap out of foamboard without the weight.

Read over the plans a few times. Eye some screen captures. Read message boards for techniques others have employed for making a trap.

Believe it or not, a lot of work goes into just paper and pencil type research.