Before you do anything make sur eyou know exactly what is leaking. HAve somepone run some water while you look underneath. In my case it was a cracked pee trap, when ot was replaced everything was fine.
There is a tool to remove that drain available at Lowes or Home Depot or ACE. IT has a T handle and prongs on the other end that fit into the "spokes" you will see when you remove the strainer from the drain. Insert the tool into the "spokes" and twist and it should unscrew w/o much difficulty.
The pee trap end which goes into the drain pipe after the "trap" should just unscrew it would be a slip flitting with a washer which crushes a bit to seal when it is tightened. Unscrewing the drain at one end and the pee trap at the other should facilitate removal of the entire piece if that is necessary.
I do all my own stunts
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Doc(He's a PhD)