If you have a tiller, till the soil several times allowing seeds to germinate in between tillings. This will be a big help with weeds that use seeds to reproduce. If you have weeds that use rhizomes, that is a whole different problem.
I suggest you try tilling, rent one if you have too, but it seems to me that you need one if you want to pursue this garden hobby.
After you till you need to root through the soil and see if you find rhisomes, they look like little potatoes with roots. If you find these remaove as many as you can. You will have to use a herbicide, a premergent.
I don't think that removing dirt is necessary or a good idea.[/QUO
TE]
That is kind of what I have done this time I used a small tiller that attaches to my weed eater and grab the bigger pieces. I guess a little shot of round up on them as they come out will do the trick I will try the pre-emergent as well