Typically, you don't need to cut the countertop to install an LG dishwasher, since the alcove to house the dishwasher is usually built into the kitchen. However, if a new unit is too tall to fit the alcove, simply cut the counter with a reciprocating saw.
If the dishwasher is not too much taller than the space provided, use a reciprocating saw to carve out some of the cabinet material to make room for the dishwasher. Do not cut into the plywood deck of the countertop, since it is the main support for the counter. If the dishwasher is too tall and therefore requires cutting into the plywood deck, install it inside a cabinet box instead.
Once you trim the bottom horizontal surface of the countertop to fit the dishwasher, prepare the electrical and water connections. Make sure to turn off the electricity and water supply before starting. Slide the appliance into place, making sure the feet are level. Connect the water supply to the machine by pulling the hose up through the bottom of the dishwasher and fastening it using an elbow inlet and compression fitting. Next, pull the wires through the bottom of the dishwasher, and connect them to the matching wires in the dishwasher.
Place the panel in the bottom of the dishwasher, and then cover the water and electrical connections. Screw the dishwasher into the brackets.