Well, that planting area has to be graded to fix the drainage first. If it is legal where you are I guess you could install drains going to the street but I could never get away with it any places I have lived in the US.
Your next step has to be to till the soil and fold the amendments into it. It will be some work but you may have to do it with a shovel. Then level it out with rakes.
Just a question? How set are you on a 240 sf lawn? Would some mix of low ground covers, ornamental grasses and so forth work?
By the way is this area sun or shade?