Nuke these weeds!

Well, You can spray with a weed killer that doesnt leave a risidual, such as Roundup, or other brands.But then you have to wait for the weeds to die and then you will still need to remove them, or you can use a good tiller and till it up and remove weeds that way,Thi will be the quickest way. Good luck feel for ya.

You're going to have to actually put some real effort into this. I know it's a drag, but it is what it is. The best way is to till the dirt,pick out any weeds you see, wait a few days, repeat the process, wait a few days, and repeat the process again. This gets rid of the weeds and then kills the new ones just germinating. It's pretty much an on going thing. There is no such thing as a weed free garden. It has to be worked at. If you dont have a tiller, then you'll just have to do it the old fashioned way and pull by hand or use a hoe.
As far as poisoning the weeds goes... Why would anyone want to ad poison to the earth. Besides that, it's a short term solution. As the previous poster noted, you'll still have to pull the weeds out. Then you'll have to keep repeating the process.  Not to mention the expense of buying the chemicals.
Once you've gotten rid of the weeds and planted your garden, take the time and spend the money to mulch it well. This will drasticly slow down , if not prevent the weeds from returning. The added bonus to this is that it will protect your plants from the high summer temperatures, will save water and will condition the soil (assuming you use a natural mulch, such as shredded tree bark, hay, etc)
Good luck and happy gardening.

not chemicles they can kill your plants use a weed burner or simply weed it

Sorry I'm too late for your question for this year, but, you might, in the future, try lasagna gardening...using 4-6" of wet newspaper ON TOP OF where you want to plant(6" works best).  Then add lots of soil, compost, etc. on top of the paper.  And do not forget to mulch like crazy after you have planted!  I love this way of gardening...kills weeds AND I don't have to dig or use weed-killer! Makes really great earthworms, too, and I can recycle my newspapers(or cardboard). And the 'BIG PLUS'?  My back doesn't ache from digging! :o)  I have made several large and small beds using this method here in my own gardens and for my neighbors.(also, I have read where many others are catching on lately to this great way to garden). Now remember, the weeds will show their little pesky heads occasionally because (a) birds will poop weed seed into your beds during their flyby, and (b) hey! they're weeds, known to show up where not wanted!  But with this method of planting, the weeds are super easy to extract, especially after a good rain or watering.  I hope this helps and that your veggie garden turned out lusciously this year! :o)

I would mow down the weeds, deep till the garden and rake out the debri.