A standard cup plunger (not a flange toilet plunger) and a wet rag.
Plunging a double sink requires a specific technique to ensure suction reaches the clog rather than just pushing air to the other bowl. double sink clogged
A double sink clog is a nuisance, but in 90% of cases, a dry plunge or a P-trap cleaning solves it in under 15 minutes. Good luck A standard cup plunger (not a flange toilet