Just like in the title. I heard about 3 sisters (corn, squash and beans) planted in one area in the correct order (first corn, then beans and then squash). Also radishes with carrot. Radishes are ready when carrots are very small. When you collect the radishes you let the carrots grow, but can't plant next radishes as carrots will be too big. Got any tips like this?
Onion sets near broccoli--harvest the onions when the broccoli plants get big. (Works with cabbage, cauliflower, anything else that starts small but gets big before it's ready to harvest.)
I think the single best space-saving technique is to think about how much you really want to eat. One zucchini plant will always take less space than six zucchini plants. One or two tomato or pepper or broccoli plants will always take less space than an entire row of each. A dozen lettuce plants don't need as much space as a hundred lettuce plants. Even if you want to freeze, can, or dry the produce for future use, you can practice with small amounts the first year.
Certain crops will be easier for you to grow than other crops--and which ones are easy for you will probably not match which ones are easy for someone else. So if you try a little bit of many things, you learn what your easy ones are. You may have different sunlight, soil, bugs, and even climate than your friends and neighbors do. For example, in my own yard the ground slopes and the house & fence affect the flow of warm/cold air. So my "first frost" might happen several weeks later in one part of the yard than another.
I also recommend looking at Square Foot Gardening. You don't have to do everything the way the guy recommends, but he does make a very good point that you can have a garden with two tomato plants, one broccoli, a dozen carrots, and so forth. And he's figured out a way to give them all the right amount of space no matter how you mix them up, by dividing the garden into one-foot squares and figuring how many plants fit in each square (or how many squares per plant, for a few big ones.)