How do I clean out and get rid of smells coming from the sink?

Clean out the P-trap beneath the sink and check there is water in the trap. If there is no water in the P-trap it allows sewer gases to come into the house. https://www.youtube.com/watch?v=D01nuMq-Lc4

Lemishine makes a disposal cleaner or pipe cleaner that works really well. If the kitchen sink, I use orange or lemon peels in the disposal side.

For bathroom sink

pour ½ cup baking soda into the drain opening.

Pour ½ cup white vinegar into the drain. ...

Pour 1 gallon boiling water down the drain to flush out leftover residue.

Repeat every once a month or as necessary.

https://youtu.be/xiuKTOkbF_o

If I smell anything, I put some baking soda in the drain, pour vinegar over it, pouring boiling water until it drains easily after the baking soda dissolved. When I clean my sink I often squirt Dawn dish detergent (just a drop or two) and run hot water to flush it through. No odors.

1/2 box of baking soda and peal a whole lemon with a grater and put down the drain then add 1/4 cup white vinager let sit 30 min then rinse with hot water

Get an enzyme cleaner from the grocery store. It will help eat up what ever nasties are in there making things funky.

I put baking soda down mine and then wash that down with vinegar. Let it sit for 10-15 minutes then dump boiling water down the drain. Followed by lemon chunks.

Also could be an issue with an old hot water heater, if it hasn't been drained in a while, it could cause that stink

Remove as much as possible with a snake or drain cleaning tool. Pour ½ cup baking soda then ½ cup white vinegar in the drain and cover, letting sit for 20 minutes. Boil water, remove cover, and pour water down the drain. You may have to repeat the process.