Remove the drawers and hardware from a small dresser. Remove the back of the dresser in one piece and use it as a template to cut a piece of quarter-inch-thick plywood to the same dimensions. Attach the wood to the back of the dresser with finishing nails and a hammer.
Measure the length and width of the top of the dresser. Have a piece of butcher block cut to these dimensions. A lumber yard normally makes these cuts for free or inexpensively.
Sand the drawer fronts and the entire dresser, including the new back, with 80-grit sandpaper, and then finish with 200-grit sandpaper. Wipe away any sawdust with a damp cloth.
Apply a thin coat of semigloss paint with a paintbrush or small roller to the entire dresser except the top. Paint the dresser drawer fronts as well. Allow to dry, then apply a second coat. When the second coat is dry, apply a coat of clear varnish over the paint.
Turn the dresser upside-down on a work surface. Attach a locking castor wheel to each corner of the bottom, according to manufacturer's directions. Lock the wheels and turn the dresser right-side-up again.
Apply a layer of construction adhesive to the top of the dresser and set the butcher block on the adhesive, according to manufacturer's instructions. Allow the adhesive to dry. To move the counter, unlock the wheels and roll it to where you need it. Lock the wheels again to stabilize the counter.