Hair on the stopper rod
The pop-up mechanism catches hair just below the drain opening.
Water sits in the basin and drains in a slow swirl, sometimes with a gurgle or smell.
Short answer
Hair and soap caught on the pop-up stopper are the cause in most cases. Pull and clean the stopper first. If the sink is still slow, the P-trap or the drain arm into the wall is packed with residue, or the vent is not working. If more than one sink is slow, the shared line is the place to look.

The pop-up mechanism catches hair just below the drain opening.
Toothpaste, soap and shaving cream harden in the trap over months.
Buildup in the overflow channel slows drainage and causes odors.
A blocked vent makes the sink drain in gulps and gurgle.
Older Miami homes may have galvanized or cast iron drain arms in the wall that narrow with scale. A small auger clears them, but a badly scaled arm may need replacing. The sink drain cleaning page explains what a plumber does once the stopper and trap have been ruled out. Adjusting the pop-up linkage under the sink can also help: if the stopper never lifts fully, water drains slowly even with a clean trap.
Call when the sink stays slow after cleaning the stopper and trap, both sinks in a double vanity are slow, it gurgles constantly or you notice a sewer smell.
Hair and soap on the pop-up stopper.
It can loosen light buildup but rarely clears hair. Removing the stopper works better.
Yes. Residue trapped in the overflow or trap starts to smell. Cleaning both helps.
They share a drain in the wall, so the clog is past where they join.
It lets water drain if the basin fills. Cleaning it with a small brush can reduce smell.
Not directly, but standing water can find worn trap washers. Check under the sink.
Usually, with a bucket under it. Hand-tighten the nuts when reassembling and check for drips.
Air is being pulled through the trap by a partial clog or a vent problem.
Not directly, but a loose pop-up linkage from the faucet's lift rod can keep the stopper partly closed.
A grid strainer or push-button drain catches less hair and is easier to clean.