I'd probably opt for raised beds in your situation. If only because I'd want to get the soil tested before planting any veggies directly in it so close to the house.

Smart to start ASAP as planning is the key to success. Here is a helpful article about starting a veggie garden: http://www.tomatodirt.com/starting-a-vegetable-garden.html. You can look at the links to 3 types of rows, too. I agree with SpoutingLexi that raised beds would be excellent in this area. Make sure you have enough sun. You'll want to angle the rows to take advantage of the sun given the fence.

Here is a link that might be useful: Starting a Vegetable Garden

Thanks for your tips, very helpful!:-) This is what was under 3 layers of tarp. My husband says just plant the seeds in the dirt, but I do know i have to loosen it and work in some new soil. What do you recommend? By the way, I still favor doing raised beds, but my husband is hesitant, he won't be doing any of the gardening:-) How is soil tested?

Find your local agricultural center for a soil test. They should tell you how to take it and explain the results.

Are there any utility lines located in the area?