First you can drain the sink by putting a bucket under the p trap and loosen the nut until you have drained the water. You will have to be careful when doing this because you put a chemical drain clener in the water which never works. If you have a clean out outside you can open that and drain the water.
After you get the water out take the trap apart and see if the clog is just in the trap or the pipe that goes to the wall.
If the clog is further down the line you will need a hand snake or a power snake to run the snake down the line to unclog it. Or you can use a sewer rod to run down the line.
One thing that will not work even though they sell the stuff is a chemical drain clener it just will not work.
Thank you for your answer. The U-shaped pipe underneath the sink does not have a trap with a nut so that I can drain the standing water.
What do you suggest?
You may use a shop wet vac to remove the water. Do you have a garbage disposal?
Ok then the best thing you can do is get a hand snake and with this you run the snake down the drain to unclog the line I will post a photo of this soon.
Ok then if this is the case then you will have to get the water out of the sink one cup at a time then use a sponge to get the rest. When that is done you will have to cut the pipe below the sink to run the snake down the pipe and you will have to put that pipe back together when done unless you can get to this pipe from under the house or outside.
You can go up on the roof and run the snake down the vent pipe when up on the roof you will have to be very careful up there.
Your welcome for my time
And if you do not have the tools to do this you could always buy or rent then.