Here is my process:

Goes without saying... But, just in case there's a newbie... remove the shoelaces.

1 Clean the shoes.
You can't shine dirty shoes. So, first... clean them completely. I do this with good old fashioned soap and water. I run warm water in the kitchen sink and use baby shampoo on an old soft toothbrush. Obviously, don't soak the shoes. I just run a tiny stream along the seam between the upper and the sole where dirt builds up. I wear Dr Marten boots and like the yellow stitching to stay bright and yellow. Rinse thoroughly and then dry thoroughly. Now that the drying rag is slightly damp, use it to remove and dust, dirt, debris. This is a good time to clean the bottoms of the shoe as well.

2 Clean the leather.
I used to use saddle soap. However, I think it's a bit harsh and switched to Meltonian Leather Balm. It's a cream that serves as a cleaner / polisher / conditioner. I rub it in with a clean dry cloth and then wait about 12 oz. (get it?) for it to soak in and dry and then use a fresh part of the rag to polish it off. It's the same process as the final polish but you'll see some dirt and grime coming off.

3 Apply the wax.
I use Lincoln brand wax. I used to use Kiwi. I tried several different brands and determined that Lincoln really is the best. I use an old T-shirt cut up into 2 square rags. I soak it thoroughly and then wring it out thoroughly. A wet application is the key. Wrap the rag tightly around your finger and smear some wax onto the cloth. Smear it on the leather lightly. Be sparing. A good guide is that if your finger is getting black under the cloth - you may be using too much polish. Let one boot dry while you start the next.

4 Polish.
Spray a fine mist of water over the leather using a spray bottle. I use an empty windex spray bottle - it has just the right misting spray nozzle. Wrap a fresh rag (soaked and wrung out) tightly over your index and middle finger and polish vigorously. Really get into and get some friction and heat up.

5. Repeat the application and polish.
Use a moist rag to apply and moist rag to polish. The second time polish with a lighter touch. Be sure to spray a fine mist of water over any surface before polishing and use a fresh, clean part of the moist rag. Don't let the rag ever get dry.

6. Repeat the application and polish.
Moist rag to apply, spray a fine mist of water, moist rag to polish. This time a lighter touch. The first polish was getting the wax deep into the leather. The second polish was getting a good base shine. This time around it's a buff shine.

Lay them out overnight and then in the morning use a moist rag to give a final quick rub down. Run the shoe laces through the moist rag and restring. You're good to go.

I've been wearing Dr Martens boots for over 20 years and am only on my second pair. First pair went for about 15 years - the sole wore straight through before the leather even got the start of a hole. I don't wear them lightly. I'm rough on these things. With proper care and cleaning you can get a lot of wear from leather.