Cate, I'd tell you to take a spade and start digging, beginning at the edge and working your way in. Clear the whole area - have a 'keep' pile and a compost pile. Once it's totally clear and you've gotten all the weeds and roots, add some compost and re-plant the desirable plants. I'd ask for help - this is a tedious task and giving up is one's first thought, but it's SO worth it when it's done!

Come back and show us pictures of your progress.

Cate - exactly as kayjones says except I'd change the word 'spade' to 'fork'. Much easier to sift the earth from the weed roots, lighter to use and easier to insert in harde soil. You don't say how 'small' the plot is - can you let us know? BTW - you ask for the obvious. So remember you are working backwards so you don't tread on the newly dug ground. But check behind you before you move your feet so as to avoid standing on plants you want to keep.

Hi:) I'd like to add I am facing a similar situation, except Cate mine isn't as grown over:( Wish I could help you!. We've just moved into a house that has a nice, "mulchy" garden spot but is covered with weeds. The weeds have been moved down (into the garden spot.)

So....it's the last of June; do I just plant into the plot and heavily mulch over the weeds or what would you advise?