Turn the table upside down and attach the casters.
Take your frame to a framer, if necessary, and have it cut down to fit the top of the table. You should be able to screw the frame to the tabletop. Don't worry about the glass, you won't need it.
Attach the cabinet handles to the top and bottom of the frame with screws. These will help you move the trolley around.
Cut the piece of wood to fit inside the frame and sand it. Use the primer and paint or stain to decorate it as desired. Fit the wood into the frame and nail into place.
Use the miter box and jig saw to create a guard to fit around each shelf. These shelves will hold baskets or cookbooks. Sand, prime and paint as desired. Attach the guards two inches from the top of each shelf.
Attach the frame with the wood insert to the top of the table with screws.