Step 1:

We shut off the water before we did anything and then turned on a couple faucets to try to get all the water out of the pipe we could. Then we removed the saddle valve and cut the pipe as shown in the picture below using this sweet "Auto Cut" device we found at the store. It took just a minute or two to cut the pipe. We made sure to cut out where the hole was from the saddle valve and also to make sure it was the right size so that the T coupling would fit nicely.



This picture was taken after we cut the pipe, but all you do is snap the cutter on the pipe, twist it a few times, and the pipe is cut. Here is a picture of the cut we made: