How do I fix my garbage disposal / sink myself?

Hi I need some help with my kitchen sink. I dont have the money for a plumber and im not finding my exact problems online. please help me if you can. whats going on is there is standing water in the bottom of my dishwasher. at the same time the kitchen sink wont drain and when it does it drains veeeeery slowly. by turning on the disposal it drains quicker but as soon as I turn it off the drain vomits up a gallon or two of dirty water from the pipes bellow and the bottom of the dishwasher. plus the disposal doesn't sound normal. It's dulled and doesn't seem to be running right. in a family house of 5 not having a sink and dishwasher is not going to work. the kitchen is already filled with pots and plates. please help me if you know whats wrong with my sink and know how I can fix it myself. thank you so much.