Depending on the size of the area, the quickest way would be to use a sod cutter or flat shovel and strip off what is there.* You could use what you remove to start a compost pile.* You can rent a kick or power sod cutter for a half day or a day.* Here's what they look like.
Power sod cutter
Then add 3" to 4" of compost and or mix it in with a shovel or till.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.