How about container gardenining (lots of people garden in 5 gallon buckets) or building raised beds? That will give you fresh soil that the plants will thrive in and minimize your wedding areas.

I made raised beds and brought in nice compost/soil to start with. It is easy for me to weed my beds, as the soil is soft and the beds don't require as much bending over.

You first water the garden heavily, then pull the weeds, shake the dirt off of the root ball and throw the weed in the garbage or a hole at least two feet deep.

In the fall turn the garden over with a shovel or roto-tiller.

Then cover it with some type of amendment preferably animal manure based.
You can do the minimum till schtick only after you have improved your soil.
If you soil is poor, newspapers and cardboard will merely give you poor soil covered with newspaper and cardboard, unless you have years to kill waiting.

If your weeds are that bad use some chemical weed killer and stop beating your head against a wall.

LoLauren,
Thanks so much! We have tried some of that that, but budgetary concerns have interfered with doing a really good job all at once, and what we have been able to do seems to disappear into the clay in a matter of months.

I did decide to never, ever, ever, try to grow tomatoes in that soil again--I can put them in containers!

philothea,
I find a thick (at least 5inch), regularly reapplied, natural mulch basically stops the weeds.
Apart from that, it protects the soil and plant roots,gets worms up aerating the surface and it will also bring about world peace ;)
I use basically whatever I have that won't blow around: weeds, grass clippings, old straw, spent brewing barley...I grow some plants specifically for mulch.

Yup, plastic has been my long-term solution to that issue. There are ways around the seed-sowing issue. The first it to grow transplants of anything that can possibly be transplanted, which is actually everything except the vast majority of root crops. The other way to sow seeds in plastic is to do small cutouts to allow the minimal possible exposure for weed sprouting. I've done holes roughly 3 to 4 inches across, or very narrow rows about the same width. The main key is to have it anchored extremely well so that wind can't blow the plastic around and smother out/cook from solar heat the seedlings.

Mulch...

You've providing an unnaturally fertile place for anything to grow (a garden bed).

You're never going to stave them for nutrition or water...you next stop is to deny them light. That won't help stuff like nutsedge, but you'll have a lot less to deal with (including the light-excluding germinating weeds) as the years roll on.

I understand your frustrations. Before you give up, I would suggest the following:

1.) Not all soils are conducive to gardening. Based on research you need to decide if this is your case. If you consider this to be fact then go to raised beds or containers, or find a more suitable location for your garden.

2.) If you decide that your soil is suitable for gardening then I suggest that you reduce the size of your garden to an area that you can manage fairly easily. Better to have something than nothing at all. As you succeed you can add back a little bit of gardening space each year if you so desire.

3.) Till or spade in compost, rotted leaves, grass clippings, etc. in fall. Organic matter in the soil helps to keep it loose and friable. Till or spade again in spring before planting when soil is fairly dry. Minimize walking on the soil after tilling and throughout the season to reduce compaction - have paths and stick to them as much as possible.

4.) Mulch the garden with weed seed-free mulch or a man-made product. Find something that works for you - there are lots of ideas and methods discussed in the GW forums. If you do not know how to do a site search on GW then check out the FAQ or ask. Do your research - knowledge is your best weapon against gardening issues and problems.

5.) Weeds are a fact of life and they will always be in your garden. Get them when they are young and small. Give your garden the constant attention it deserves to control weeds but also to spot disease or pest problems. Gardening is a commitment. A gardener can not "take time off" and ignore the garden for a week. Get into this habit and it will surely fail and all the work will prove to be a waste of time and effort.

6.) Purchase a few vegetable plants rather than trying to start them yourself. Starting plants is another big step in gardening and requires knowledge and equipment. This seems to be part of your frustration so put it aside for now. If budget is tight, set aside a coin jar to save up for purchasing or barter with a neighbor gardener for starter plants if possible. Just get a few plants of the common varieties in the cheaper multi-packs - again, better to have something than nothing.

7.) Common vegetable varieties available as seeds or plants are common for many good reasons. They are usually some of the easiest to grow. Stick to them for now and experiment later on with more unique or rare varieties.

8.) Post questions in the forums on GW and provide pictures if possible. You are among helpful gardening friends here. I am the first to admit that I do not know everything about gardening. When I have a gardening problem or concern I have always found answers here or at least leads to be able to do some further internet research.

Success will bring back the excitement and joy of gardening in you. Give it another try.

Good Luck!
-Tom