Once the screws are removed, yank up on the trip lever and the whole mechanism will come out.
Look for hair or debris that can be removed. Now that the trip lever has been removed, a hand snake can be used.
Before plunging, use a wet rag to block the hole in the overflow plate where the trip lever is (Image 1).
Next, put a few inches of water into the tub, then hold the rag in place and start plunging (Image 2).