There are many ways to fuse the spine depending on the condition of the bones, number of levels involved, and training of the doctor. All methods involve putting bone graft between the vertebrae. In general terms the three-step process you are asking about probably refers to an interbody fusion.
Interbody fusion means two vertebral bodies are fused together. The steps include: 1) remove the damaged disc material, 2) insert cages and/or graft material in between the two vertebrae, and 3) support the healing spine with screws, plates, or rods to hold it together.
The last step is called instrumentation. Instrumentation can be used to fix a deformed or curved spine. For a spinal fusion it's acting like a splint inside to hold the bones together while the bone graft heals.