I love having a vegetable garden but I HATE weeding. This is a trick I learned from my folks after years of pulling weeds in their garden.
Step 1: Gather LOTS of newspaper
Save your newspaper. Grab them from work. Solicit them from you family, friends an neighbors. The bigger the garden, the more you will need.
Step 2: Stockpile grass clippings
It's best to use fresh clippings since they tend to mold if you keep them in a pile for too long. It's better to have too much than not enough.
Step 3: Plant your garden
If you are starting with seeds, you will need to wait until they are at least a few inches high. Mark them well. If you are starting with seedling, then you can skip right to the next step when you are done planting.
Step 4: Lay out the newspaper and cover with clippings
Lay out your newspaper all over the garden 2 - 3 sheet thick. Get as close to the base of you plants as you can. Layer the newspaper with 4 - 6 inches of fresh grass clippings. You do not want to see any of the newspaper when you are done. The weight of the clippings should keep the newspaper from being blown away by the wind (gale force excepted).
Step 5: Water your garden
Give your garden a good soaking. This also helps keep the paper and grass from flying away and gives your plants a good drink. The space you left around the base of the plants allows plenty of water to get through immediately while the grass and newspaper will allow the water to soak through more slowly.
You may need to do some minor weeding around the base of the plants but for the most part 95% or more of the weeding you normally do will be eliminated. Add more clipping during the year as needed. At the end of the year, rototill the clippings and the paper into the garden. No need to pull anything up at all. I find this works many times better than just clippings alone.