Find the specifications for your outboard, particularly the weight, in the motor operator's guide. Move the outboard until it's beneath a rafter, beam or other overhead support capable of holding the weight of the motor as you lift it.
Slip the hook of a chain fall -- a block and tackle that's rigged with chains instead of rope -- through the link at one end of a piece of case-hardened chain. Use chain that is rated for twice the engine's weight and long enough to wrap around the support beam.
Wrap the case-hardened chain around the beam and insert the chain fall's hook through one of the case-hardened chain's links, to secure the chain fall to the bottom of the support beam.
Find the latch for the top cover of the counter-rotating outboard. The latch is typically on the back of the top cover and either twists or lifts. Activate the latch and lift the top cover from the motor. Set the cover out of the way.
Inspect the top, center of the powerhead -- the "engine" part of the outboard -- for a lifting ring that's lying flat at the center of the engine. Raise the lifting ring. Insert the lifting hook of the chain fall into the lifting ring.
Raise the outboard, using the chain fall. Back the boat under the outboard so it's over the position for the counter-rotating outboard. Lower the outboard so its bracket goes over the transom of the boat. Push the counter-rotating outboard so the mounting bores in its bracket line up with the mounting holes in the rear of the boat.
Insert the counter-rotating outboard's 1-inch mounting bolts through the 1-inch stainless steel washers. Push the bolts through the mounting bores of both mounting bracket and boat. Place a second stainless steel washer on the bolt. Thread the 1-inch nut onto the bolt. Tighten the nut to 55 foot-pounds with a torque wrench. Repeat for the three remaining mounting bolts for the counter-rotating outboard.