You will need a table saw (or circular saw), drill with screwdriver bits, jig saw, (miter saw, if you have one available), router with a 1/16" slot cutting bit, and at least one pair of clamps. A pair of sawhorses is also greatly recommended. You will be generating a lot of dust so, if you construct it in your garage like I did, don’t plan to clean your house until after you complete your cabinet.  In addition, make sure you have safety glasses.

If you have access to a orbital sander, get it.  I did not need one but you may.

[Update- I purchased a table saw to help with later cabinets and would recommend it, if your budget allows.  This is a low-end model that Lowes sells for less than $180]