Hi!
Welcome to the forum.
Since you don't have much prep time this year, you'll need to get busy pretty quickly.
Probably don't have much time for a soil test and may need to wing it. You don't say. Is the garden in full sun?
If so, I'd start small with warm season crops, maybe do some fall crops as well, but mainly work on summer crops this year and prepare your soil for a bigger garden and more crops next year. You can conceivably get three crops out of a garden in Oklahoma, but you want to prepare your soil first. DO NOT use fresh manure in your soil if you are getting ready to plant as it will be too "hot" and will burn your plants. It will also bring weed seeds in that you don't want.
One of the best books I've ever owned is the Encyclopedia Of Organic Gardening. It was the first book I ever bought and was my bible for many years, so I highly recommend it.
The following crops are cool season and will bolt (grow to quickly and quit producing) quickly when the weather gets warm, which it seems to be doing very quickly this year.
I'd save these for fall planting or for next spring: radishes, spinach, carrots and broccoli.
The rest can be planted between now and the second week of May. You could actually plant some beans every week, just to ensure that you don't have a big flood of beans and then none for the rest of the summer.
Interplanting, or companion planting in wide, slightly raised rows that are wide enough that you can reach the center from either side is a good plan.
You can and perhaps should first dig up the plot with a shovel and remove the weeds before tilling in plenty of good quality, weed free compost. Till north to south and then east to west, to be sure you get the compost tilled in very well.
Once you have the entire garden tilled, rake the soil into beds and leave paths between the rows the same width as your rows. Lay down clean straw, black and white pages of newspaper, old carpet remnants, or purchased cedar mulch about 4-6 inches deep in the paths.
Rake the beds nicely so you don't have any big clods. Then you can either plant seeds or put in transplants.
When you buy your green beans, be sure you also buy innoculant and follow the directions on its use. Horns or TLC or any good nursery or coop will tell you why you need to use this. Also buy bush beans and bush type squash and pumpkin. You will have plenty of vines all over your garden with just the watermelon!
Within the beds, hill up the soil and plant a couple or three squash or pumpkin seeds, about five bean seeds and a corn seed or two all in the same hill at the correct depth on the seed packets. Plan on planting at least a dozen or so hills, about two-three feet apart, and realize that you will probably have to flood irrigate the hills, so make little motes around each hill.
Planting all these together is good for a couple of reasons. Corn is a heavy feeder and so are squash and pumpkin. They use up a lot of nitrogen. Planting the beans with them helps fixate nitrogen into the soil so both squash and corn grow better. And, often one plant will offer insect repellant for another. Planting Guardian marigolds in among your plants, for example, will help ward off some bugs. Interplanting with garlic and onions and chives is good as well, although onions and chives need to be planted early and garlic has to be planted in the fall.
Interplanting like this, with these particular crops, is a tried and true Native American method that really works. Using fish emulsion mixed with water to fertilze the corn and squash will also help. Native Americans also used to put a dead fish deep in each hill. This provided nitrogen for the plants as they grew.
Unless you have very sandy soil or want to add sand to a bed, the watermelon may have a tough time in clay. I would put it into one end of your garden.
Watermelon also grows best in hills with motes, with three or four seeds to each hill. You may want to thin these if they all sprout and grow, down to one or two plants.
If a heavy rain is predicted after you plant and before anythig sprouts, you might want to put a little light mulch on top of the hills just to keep the seed from washing away.
Once the plants are up and growing well, you'll want to mulch with clean straw so that the moisture stays in the soil and the veggies stay up off the ground.
Squash, watermelon and pumpkin take a lot of water and so does corn. And, so do cucumbers, or cukes.
Cukes also need rich, deep soil. If you have a wire fence, dig about two feet down and add plenty of compost to form a good, deep bed along that fence and let the cukes grow up it. They, too, will need lots of water.
You could also grow bush type cukes if you don't want to mess with growing them up the fence or providing a trellis.
Hope all this helps!
I'm sure you'll receive plenty of other suggestions.
Google for the veggies you want to grow for other tips as well and fork out a little cash for some good, basic veggie gardening books to help you identify things like squash bugs, cucumber beetles and corn worms and learn what to do about them.
At the end of the summer, you can plant some cool season crops and see how they do. Next year, plant in this season's beds and walk in this season's paths. Rotating beds and crops will keep you from wearing out the soil and will cut down on pests. Planting a fall crop of winter rye and tilling it in early as green mulch is also a great way to improve your soil.
Again, DO NOT use green manure on your garden at this time of year. It probably has all sorts of weed seeds in it and will burn your plants. Start a compost pile now that will "cook" the weed seeds and make compost for your use next season. Have a soil test done next fall or spring as well, just so you know what you may need to add next eyar to improve your soil.
Good luck!
jp

Thanks for your reply jp. Yes the garden will be in full sun until between 6-7pm when the shadow from the neighbor's fence totally covers our yard.

My father-in-law stopped by the other day and sorted my seed packets into the "hills" and "rows" for me, so sweet of him. He has a bunch of gardening books he said I could borrow. I'm looking forward to reading them. Also, my dad was once a gardening wonder before my mom died, hopefully he'll lend me his expertise even though he stopped gardening/landscaping 8 years ago.

I don't have any compost handy around here. My husband isn't keen on starting a pile, I've already discussed it with him. We just trimmed back some branches from some trees and bushes, should I start a pile with the still green leaves from them and some grass clippings from the lawn? Also, would a local nursery sell compost by the pound maybe? Just wondering. I'm stopping by a nursery up the road this week, I'll ask and see what I come up with.

jp, thanks again for all of your advice and for taking the time to explain things to me.

Best of luck to your garden this year.
I've got a lot to do this week :)
Celeste

So glad your dad is around to help you. I'm sure you'll both get a lot of enjoyment out of the time you spend working on your new garden together. Definately borrow books from his library, especially if they are about improving the soil and designing a garden from the basic bones up.

Composting is relatively easy, just a matter of doing thin layering of green stuff with brown stuff, dry with wet, dirt, lawn clippings, manure (dry works as good as wet)and keeping it damp but not wet so it will all decompose. As long as the branches aren't any bigger than your little finger, you can break them up into small pieces and add them to the pile. Much bigger than that and you'll need to use a chipper or lawnmower. Leaves decompse fine, though. Don't make your layers of lawn clippings too thick though, as they will take longer to decompose. A few inches thick is plenty. There is also a composting forum that might help you.
However, you can also buy compost by the bag or in bulk from landscaping companies.

You don't want to use compost straight, as I mentioned before, but will need to till it in to your soil in a fixed ratio that the company you buy from should be able to give you.
Good luck!

Celeste,

You can normally find bagged compost as well as bagged, composted cow manure (thus, ready to go into the garden) at home center stores like Lowe's or Home Depot. The best compost I ever bought at a store was Mushroom Compost purchased bagged at Lowe's a couple of years ago. My favorite cow manure (only a gardener could appreciate that statement!) is a brand called Black Cow (Kow?). It is in a yellow bag and is 100% composted manure. Some bags that say "manure" on them are as little as 10% manure and a lot of filler.

Also, if your DH is opposed to starting your own compost pile, may be you can find out why and work through his objections as compost is the BEST thing for a veggie garden! (Some people don't like looking at the compost pile, but you can compost in containers...like a large plastic trash can with a lid, for example. There are compost bins available for purchase, if you don't mind spending the dollars. Others are afraid a compost pile will attract undesirable critters, but it usually doesn't as long as you aren't trying to compost meat products or vast quantities of spoiled fruit/veggies.)

Keep us posted on your veggie garden efforts. We have quite a few veggie gardeners here on the Oklahoma forum. :)

Dawn