Welcome , bud. Stabilization can be done in various ways. Basically, you have to integrate yourself fully into the dream. How? Leave your real body behind, and shift into the dream body. Some people do that by rubbing their hands (their dream hands), or by feeling around in the dream, or simply by looking here and there. Try to activate as much senses as you can. Feel around, see, hear, smell. You'll find that the clarity and the vividness of the dream will skyrocket.
Good luck, and keep at it.