I inherited this little garden area from the previous homeowners that is completely overgrown. There is some nice stuff, so I tried to tame it last year, but it's just too far gone and I want to start anew. Anyone have any recommendations to easily accomplish this? I don't have any equipment and I want to be able to plant in it come fall.

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Put a couple of overlapping layers of cardboard on it to smother what's there, water well, then add one inch of compost on top. Charles Dowding is a famous gardened that vouches for this method.

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so wait, you put the water and compost on top of the cardboard? how long till the cardboard breaks down? or do you eventually just yank it out? 
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Yes exactly. The cardboard needs to overlap quite a bit and be thick in order to completely block the light. It breaks down in a few months but you can plant before it completely breaks down by making holes where you are planting your new veggies. If it has tape of plastic on it you probably want to remove that because those bits won't degrade.