All you really need is a flat work surface, tape measure, a straight edge or carpenters square 24" is best, a screw gun, yellow carpenters glue (I like title-bond 2), a wood rasp and a jigsaw. This will let you build most basic cabinets. Circular saws, table saws, routers make the job easier and more accurate but are not a requirement to build most things. You can forget clamps if you have heavy objects around ( a 90 pound bag of sand is pretty cheap)
If you are looking to make several cabinets, I would consider a circular saw and a basic router.
Most of all, you have a vast resource here on this site. Just ask questions.