Measure the base of the tool that the base will support.
Cut 4 lengths of 2-by-4 to fit these dimensions — one for each side, and just as long.
Cut a half-lap into each end of the four lengths. Do this by cutting through the center of its thickness from the end to four inches from the end — the width of a 2-by-4. Cut in from the flat surface into this cut, and remove the scrap. Repeat for both ends in all four boards so that the ends all fit into each other to form a level support for the tool.
Install a caster wheel at each corner — two fixed at one end, two swiveling at the other — by driving 1 1/2-inch wood screws through the holes in the base plates.
Take a new piece of scrap 2-by-4 and cut it to the length of the board that has the two fixed caster wheels. Cut in along the middle of its width for at least 5 inches on either end, then out to the edge to remove two corners.
Affix the two hinges along the shortened edge of this board with small wood screws on one side; affix the other side to the baseboard on fixed casters so that the brake piece swings in and up like a pet door.
Drill a single hole through the outside of the base inwards, all the way through the brake piece on the other side.
Insert a threaded rod through the drilled hole and affix a 5/16-by-18 T-nut onto the end inside the base, anchoring it into the side of the brake piece.
Thread a 5/16-by-18 star knob onto the other end of the rod, on the outside of the rolling base's frame. To brake the wheels and keep the tool in place, tighten the knob by hand, pressing the brake piece against the wheels.
Fasten the shop tool to the base securely with lag bolts, then check the assembly with a level.