Set the cabinets with the sides lined up against each cabinet. The face of each cabinet should line up level with the face of the cabinet beside it. Clamp the faces together to keep them positioned.
Pre-drill a pilot hole between one side of the cabinet face. It should extend from the side of one cabinet face into the side of the other cabinet face to connect the cabinets together. Drill one hole in the top drawer section of the face and two or three holes in the side of the door opening's face.
Tighten a screw into the pre-drilled holes. Choose a screw just long enough to go through the side of the facing of the first cabinet and about half way through the side of the facing of the second cabinet.
Slide a spacer between each cabinet at the rear. The spacer should be about the same width of the space between the cabinets. Insert the spacer and mark where it meets the top of the cabinet. Remove it and saw off the extra length. Slide it back into the space between the cabinets.
Pre-drill a hole from one side inside of the cabinet, through the spacer, and into the wood of the second cabinet.
Tighten a screw in the pre-drilled holes. Choose a screw just long enough to go through the side of the first cabinet, into the spacer and join into the wood of the second cabinet.