If you push it down to engage it, it unscrews.

If you cover the overflow with a wet cloth while plunging the drain,that may do the trick without removing the stopper. The proper way to use a plunger is. Push down slowly then pull up smarty to begain. Progressivly increase the speed of down and up.

This is a different version of what Klem1 posted, but basically the same principle.

Make sure the trap is full, cover the overflow with a _wet_ cloth, use a wet/dry vac to vacuum the trap. Refill trap with water, vacuum again. You must cover the overflow with a _wet_ cloth, and make sure you refill the trap each time b/4 vacuuming.

Some plumber told me that one many years ago, it works.

Go to a Home Depot(other home improvement stores may have a similar product) and get the item linked.

Here is a link that might be useful: Hair snare

If it's the types that looks like a big spring-loaded button with a rubber seal around it, it does unscrew as mentioned above. The problem I always have is that the metal X bar that it screws into the center of, is a hair trap x 4. You have to unscrew the thing and remove it, then get long nose pliers or a hemostat to pull out the hair that's draped over the X. You will be shocked and disgusted at how much is hanging down into the drain.

That thing Handymac linked is awesome for hair (we have a lot of long hair in the household). You might still have to take the thingie off for best declogging.