White worms are not picky about food. Some of the things I regularly use are left over bread, Cheerios cereal, and dry cat food. Each has its own pluses and minuses. Bread is inexpensive. Cheerios make harvesting easier, and cat food has more protein and the worms tend to reproduce faster. Bread and Cheerios also have preservatives which tend to reduce molding.
Food should be moist when added to the culture. You can put it on the surface or bury it. In general burying it is best. The worms like to be under the surface, and it is less likely to get moldy. If you put the Cheerios on the surface, the worms will tend to form balls around them, which makes harvesting easy.
Once you have your worm box ready, you need to get a starter culture. Ask around at aquarium clubs. Chances are at least a few of the members who breed a lot of fish will have them.
Place the worms at one end and add a small amount of food. Check ever other day and if the food is gone add more. If the food is still there after a few days, back off on the amount you feed. The food should disappear in 2-3 days. At the start of your culture you will want to feed in the same area. As the culture grows you can increase the amount of food and spread it out more.
A new culture will be ready for harvesting in about 2 months. The worms will tend to form balls around the food. You can gently dig into the culture with a plastic spoon to find the balls if you bury the food. I use a large tweezers to pick out the worms. If there is only a small amount of dirt you can feed the worms directly. Otherwise put them in a small container of water and the worms will form small balls more or less free of the medium.
The culture medium will start to sour over time. This happens faster if you use high protein foods like dry dog or cat food. You can sub-culture the worms, but since it takes a long time to really get a culture going it is better to replace the medium a bit at a time.
My box is long and narrow. About every 3-4 months I put a cover that is only about 2/3 the length of the box. For several weeks I only feed and water the front and middle 2/3 of the box. The worms will migrate out of the back towards the food and moisture. After a few weeks there will be few or no worms at the back.
At that point scoop out the dry medium at the back. Push the remaining medium from the front to the back, and put in fresh, damp new medium in the front and start feeding at that end. This method minimizes the disruption of the culture.
White worms are high in fat, and many aquarists recommend against feeding them more than a couple of times a week. I try to follow this rule except when conditioning fish for breeding. I stopped using black worms, tubifex worms, and similar aquatic worms because of problems with introducing parasites and disease. I find the white worms are the best conditioning food I feed.