How do I unstop my kitchen sink with out calling a plummer to come out to charge me a arm and a leg to fix it.

Is it one sink or two, any way try to use a plunger, if it is a single sink fill the sink half way and use a plunger, if two sinks fill any sink and plug the sink drain fill the sink half way and use the plunger, if no help remove the trap, check for any blockage remove clean install and check, if not blockage you would need to use a snake to clean the horizontal pipe, see the image below, good luck.

John

If you decide to snake the line in the wall, (that's where we find most clogs) you will run into a bend about 8 inches in but once around that you only have to put out 6 more feet of cable. Flush with a sink full of hot water. Good luck, Tom