I would start by getting a bucket. Place it under the trap below the sink. SLOWLY begin to unscrew the trap and begin to drain the sink. You'll need to tighten back down to empty your bucket and not let it leak while doing so. Repeat until sink is empty. Once the sink is empty, take the trap off and clean it out. If it is clean, you drain may be plugged in the main which will likely require a pro with a drain snake.
To prevent this, strain your drains. If it's a kitchen without a disposal...do not allow food to be put down the drain. Hair and laundry facilities being drained into the main without straining are prime suspects. A bottle of drano once in a blue moon isn't bad as a preventative maintenance but isn't really good for your pipes. Lastly, tree roots are another culprit. If this is the case, yearly snaking or digging up the pipe may be needed.