1. Use all-purpose cleaner
Spray the shoes with multi-purpose cleaner, such as 409 cleaner, scrubbing the dirty areas with a toothbrush. Then get a towel and wipe off any excess cleaner. Keeping the toothbrush wet, continue to scrub the whole shoe until it appears white. Dish soap may also be another alternative, particularly the brand Dawn which breaks down and grease and will not stain your shoes.
2. Use watered down bleach
If done correctly, this method can be especially effective. Be sure to wear rubber gloves when working with bleach. Also, best not use bleach near a carpet or clothing as it will cause discoloration. Use a toothbrush and dip it into some warm watered down bleach scrubbing away the dark stains. This is an effective way if you have a two-toned colored shoe whereby you won't want to get the second color lighter.
3. Use toothpaste
A non-gel white toothpaste can be applied to your dirty shoe and can be scrubbed with a toothbrush. For best results, dip the toothbrush into the toothpaste, then rub it on any dirty spots on your shoe. Once it has been worked into the shoe, let it sit for about 10 minutes. Then use a damp towel to wipe the toothpaste off. Repeat as many times as needed.
4. Use the dishwasher
Empty your dishwasher making sure that there is nothing in it. Run the kitchen faucet next to the dishwasher on hot water ensuring that all the water going into the dishwasher is hot. Add your normal dishwashing detergent and put your shoes on the top rack facing downward. Run the dishwasher as normal. Once it is finished with the wash cycle, take your wet shoes out and place them in the sun. Alternatively, you can also put them in the dryer with a couple of large dry towels to minimize the shoes from hitting the dryer.
5. Use a washing machine
Prior to doing this, spray your dirty white shoes with either a carpet cleaning spray or a washing machine stain removing spray and let it sit for 10 minutes. Then put them into the washing machine on a short wash cycle using hot water. Doing so will clean your shoes and make them look like new. Your shoes will shrink a little bit so use this method as a last resort.