First I carefully used the utility knife to remove the caulking. It comes off quite easily once it gets going. Then I cleaned the "black stuff" off. Since the back splash tile was quite porous, I used an old toothbrush and some water. After it was clean, I needed to make sure the area was totally dry before I could start applying the new caulking. To speed up the process I used a hair dryer.
It was time to apply the caulking, which I had never done before. My first mistake was putting on too much caulking. So start with a small amount, you can always add more if needed. Once the line of caulking is on, wet your finger and gently run it over top of the caulking to make it look nice and smooth.
I had to do this a number of times until I was happy.
As you can see in the picture, clear caulking looks hazy when it is wet. But don't worry, it dries nice and clear so that you can hardly see it - which is a very good thing!
This took me about 1 hour and I had never done this before.
Ladies, you can do this yourself. You will be so pleased with yourself and the results!!