Start with taking out all stuff kept in the hamster cage. All food containers, water bowl and other stuff that is in the cage should be removed. Leave them safely in a plastic bin outside your front door so that their smell is not spread inside the house.
Take the cage out in the bathroom and put some baking soda in warm water. Add some white vinegar and swish the solution, and put on the surface of the cage as well. Leave the cage in the water for about 15-20 minutes.
After about 20 minutes, take the cage out of the water. See if there are stains left on the cage. If so make scrub of baking soda and rub it with a piece of sponge until the stains are removed. Be careful about the safety of hands. You should wear protective gloves while cleaning the cage, as it will protect your skin and also avoid any injury risk to you.
After removal of the stains from the cage, fill the basin which contains the animals accessories. Fill it nearly half and put a tablespoon of baking soda and white vinegar. Put the cage in the water that is sunk in it and leave it for about another 15 minutes. This will remove the left strains.
After cleaning and washing the cage, you can leave it out for a while to dry. You can also dry it up with a piece of cloth or sponge, but if it is made of steel wires, the process can be a bit risky. So better leave it dry itself, and then replace all the containers with new ones. If not, wash them the way you did the cage and put them in again. You now put back your hamster in the cage.