My sink backs up and when I try to unclog the water goes into the dishwasher. What cause this and how can I fix this.

Your drain is clogged, first use 1/2 cup backing soda mixed with 1/2 cup table salt poor it in the sink drain follow by 1 cup white vinegar, leave it over night and poor a bucket of hot water in the morning, if it doesn't help you, then looks like your horizontal drain is clogged, you need to use a snake to clear it out, good luck,

John