I've almost always washed cats/kittens by myself. Only when first doing a cat and unsure of the reaction I might have DH help me out.
First have everything you need ready and close by (within reach) - this includes the shampoo/conditioner, towels, washcloth, and if you are using a hand held shower.
Put a mat in the bottom of the tub so its not slippery - that's half your battle.
Then I run about 1 1/2 - 2 inches of water in the tub before the cat comes in the bathroom. After cleaning the eyes, ears, clipping nails and making sure all tangles are out (on a longhair), you gently place the cat in the mid to shallow end of the tub so its not too deep. Then using a washcloth I wet down the cat from the neck down (no water/soap around the face or ears).
Once the cat is totally wet then grab the shampoo and put some on the back and a little on the sides. Wash the cat with your hands and have them face the back of the tub where its not so quick to leap out of the tub.
Charlie is trained to stay when I tell him, so he doesn't just jump out. He likes his baths and complains when the water is drained.
After you wash the cat, empty the tub and turn on the hand held shower and start rinsing the cat over and over till all the soap is gone. When you can't feel soap in the coat, then kinda wring the cat out and squeeze as much water from the neck down, including the feet and tail and belly.
Have towels ready to wrap around and dry the cat. Have a 2nd towel ready when the first one is too wet. Be sure the cat (if air drying) is in a room with no open windows or drafts/fans.