Use the level to check that every cabinet frame is flush. Place the level onto each of the four sides of the cabinet frame and check for plumbness front to back, and side to side. Check each cabinet separately.
Hammer in wooden shims beneath the side of the cabinet that's too low. Continually adjust the shims and level until the positioning is correct. Repeat the process with each cabinet, ensuring that the tops of all cabinets are even so the countertops have a steady foundation on which to rest.
Place your new countertop onto the cabinet framework. The countertop should fit evenly over the cabinets, with an overhang at the front measuring from 3/4- to 1-inch deep. Use the level to check the countertop from back to front and side to side.
Insert wooden shims beneath the edge of your countertop to raise it into the proper position. Continue to place shims wherever needed, then retest with the level. Once the countertop is level from end to end, fasten it in place.