Step 1: Figure out what needs fixing
Step 2: Repair leather along sole
Step 3: Apply leather patch
Glue in some leather over the cut. You should be able to slip the patch between the leather of the shoe and the rubber of the sole. Use shoe glue that is flexible. Use suede leather that is not finished on either side. The roughness helps the glue stick. Open your window so you don't pass out from the ridiculous solvents in the glue that make it dry unhelpfully fast.
When working with leather, don't use a plastic thimble. See, the purpose of a thimble is to protect the finger that is pushing the back of the needle when you're going through a tough spot. If you push hard enough with a plastic thimble, the back of the needle may puncture your finger.