Vegetable gardens can be laid out any number of ways. The single most important consideration is sunlight. Choose a spot that gets AT LEAST 6 hours of sunlight a day.
The size and the design will depend on how much space you have, how much space you can reasonably tend and what you want to grow. No matter how you lay out your vegetable garden, remember that you can only reach about 3 feet with your arm - remember to leave ample foot paths so you will be able to get to your veggies once they are growing.
Our vegetable garden is in the front yard - the only place where we get sufficient sunlight. It's about 14'X21'. We have a single 8'X8' raised bed in the center, surrounded by 3' deep beds, with 3' wide grass pathways (wide enough to allow the push mower and the wheelbarrow through).
Last year, we tried the Square Foot gardening method which suits our small space well. Square foot gardening lays out your vegetable garden of 4'X4' raised beds in 1 foot blocks, with different crops planted densely in each area. I found this worked well for some vegetables - carrots, lettuce and radish thrived in our square foot planting. The tomatoes, beans and cucumbers which were growing vertically using a trellis did not do so well. The tomatoes, particularly, seemed very susceptible to blight.
This year, we tried a variation on the square foot method - maintaining the principle of dense planting, but giving some of the bigger plants more room to grow. Rather than 1 square foot, each tomato enjoy abouts 15"x20". The beans (about 24 plants) climb a trellis in a 9 square foot area, another 30 plants share space with the corn. The cucumbers (about 14 plants) cover about 18 square feet. The carrots and lettuce are planted densely in 1 foot rows. I think the tomatoes are still too close together this year.
The only other consideration in layout is adding beneficial plants to the mix. Onions, garlic, basil and marigold all deter pests. In our small vegetable garden, simply having these plants somewhere in the garden helps.