I did it ........ and I'm pretty proud of myself!
I snaked out my kitchen drain tonight! What a job, but I probably saved myself $100. My kitchen sink stopped draining last night, and I dreaded calling the plumber, taking off work and waiting around, only to wonder if I could have done it myself. I called my neighbor for advice (they are a wonderful family, one of the reasons I stayed in the neighborhood after my divorce, neighbors like these are keepers. Here's a picture of their having lunch with my daughter and me at Rainforest Cafe).
I did have to go to HD and get the heavy duty, 50' 1/2" snake. My neighbor tried with his small, shorter one, and it just wouldn't reach. He gave advice and took the trap off and put it back on (that's my next lesson), but I snaked that thing down 20 feet or so several times, until it moved through the blockage. My arms are like rubber.
Now, to figure out why. It looks, from the stuff I got out, that lint from the washer is getting caught in a pipe, guess that's the next problem to be solved.
Now I can run the dishwasher, and air out the house, that stuff smells awful.