Is there an easier way to kill grass?

When I moved in, the garden was a heap. There was/is no lawn and it was flooded due to the soil being so compacted.
The weather hasn't been great as of yet and so far, I have just turned over the soil and levelled it with a rake.

Where there is grass, I would like to remove it, turn it over and level with the rest of the garden.
After research, I found that by covering the area with clear plastic for 2 months will kill everything off, so that I can turn over and level the area.
Is this true?

Here is the picture;

 

That would be smothering the grass, have you ever left somthing on grass and when it was picked up the grass was yellow, same thing.
I would strim it over first anyway if that's the way you are going.

 

Thanks, guys