There may be debris in the popup drain assembly, or the trap (U-bend at the bottom) may be clogged, or there may be a problem downstream.
First, try a toilet plunger. Fill the basin halfway and give it a go.
If that doesn't do it, remove the white nut at the back of the drain tailpiece and pull out the lever. Now you can lift the popup drain plug out and see what's what. Here's what that system looks like:
When you reassemble it be sure to engage the loop in the drain plug. Don't over-tighten the plastic parts.
If you still don't have good flow, disassemble the trap using a rubber jar opener for grip and clear it. Turn the nuts counter-clockwise looking from the side with the rounded edges. If necessary, a slip-lock or locking pliers will help, but protect the chrome with a rag.