I haven't done this, but a friend who has says you can't plant them all at the same time, which appears to be a common mistake, as the beans start growing faster than the corn. This is her method:
Plant the corn first, four or five seeds in a small circle. Plant each group about four feet apart in a block of at least five sets each way.
When the corn is 10-12" tall, plant six pole-type beans in a wider circle around the corn, about 6" away. When they are well up, thin to three bean plants.
When the beans have sprouted, plant the squash seeds (running type, not bush, and usually winter varieties that will keep) in the center of a square formed by four corn/bean sets.
One observation she made was about the mounds that everyone seems to want to plant them in. The standard idea is to make flat mounds, about 20" across at the base and 10-12" across the flattened top. She said in the dry conditions of the Southwest, she just can't believe the Native Americans planted in mounds. While they may warm up faster in spring, they also dry out incredibly fast. She said she has read that the Southwest Natives planted in shallow beds, either excavated about 4" deep, or they mounded up the soil AROUND the growing area, to keep the precious water confined to the
root zones. She said these are BEDS that are recessed or have mounded edges, not individual
wells like people often make for tomatoes (etc). Once she started doing it this way, her plants did much better.
It took her several years of trial and error to come up with this method. Maybe it will help you. But always keep in mind that you may have to adapt standard ideas to suit your personal soil and climate.
Sue