Step 2: Comfort and calm the cat once in the water.
This part is somewhat dependent on the cat. How confident and trusting they are. Once you are in the water, hold the cat close and firmly to your body. Grasp the rear feet firmly in one hand. This will reduce the chance they can turn around and scratch you if they to try to get out of the water.
Use whatever petting stroke, or other type of touch that calms your cat. Stay in the position until your cat is calm in your arms and does not appear to be bothered by the water.