A kitchen sink can clog from grease, food debris, or buildup in the trap. Without chemical drain cleaner, the most useful sequence is removing accessible debris, using mechanical pressure, and checking the trap only if it can be done safely.
Remove standing water and clear the opening
Scoop out enough standing water to work without overflowing the sink. Clean the strainer or stopper and remove visible debris before inserting tools deeper into the drain.
Try a sink plunger
On a double sink, seal the second basin firmly. Cover the drain with enough water to seal the plunger cup and make several strokes; alternating pressure and suction can move a soft blockage.
Check the trap only if no chemicals are present
Place a bucket underneath and remove the trap only if you know how to reassemble it. Never open a trap after chemical drain cleaner has been added because caustic liquid may still be inside.
A deeper blockage needs a snake or service
If the trap and opening are clear but the sink still will not drain, the blockage may be in the wall line. An appropriate snake may reach it; if multiple drains are affected, call for professional diagnosis.