To build a small cabinet with drawers, obtain the materials, measure, and cut them to fit the dimensions indicated in your plan. Connect the panels using glue. Use screws and butt joints as well to ensure better connection. Assemble the shelves, and insert the drawers. Place the cabinet in its location, and attach it to the wall using wall studs. Buy the doors, if your design requires them, and hang them on the cabinet.
Assemble the cabinet starting with the base, top and bottom panels. Add side panels and finish by attaching the back panel. To reinforce the connections even further, attach corner brackets and screws.
To install the drawers, mark the height of the shelves on the sides on the cabinet. Make sure the marks are leveled, attach two corner brackets per drawer on each side of the cabinet, and put the shelves in.
Always draw up a plan before starting to build cabinets, even if they are simple. Use measurements from a different cabinet or find some sample plans on the Internet.
Make the wooden parts of the cabinet from plywood or medium density fiberboard, as these materials are cheaper. Hardware can be relatively expensive, so see if you have any used hardware at home or research a cabinet design that requires minimal hardware.