Square foot gardening
This. Definitely start here.
Similar is Cubed Foot Gardening (Christopher Bird) - also good except for his inexplicable recommendation to use styrofoam cups as seedling pots.
I also like Carrots Love Tomatoes and Great Garden Companions.
Basically, you don't need to know much except the cardinal rule: Compost, compost, compost. Don't waste your money on fertilizers that will throw the entire ecosystem and your plants out of balance. Add a bunch of compost to your soil when you plant. Replace as often as possible. Take care of your soil and critters and the plants will take care of themselves.
What you should read up on is not how to grow veggies (they will teach you!) but how to generate enough compost. That is the real challenge.