That is where you begin
I have done a few of these and until recently, I never had a case spreader which is what the pros use. You may be able to reuse the press on carrier and pinion gear bearings if you can get them off the old ones, but I have always bought new.
The one thing I found to be invaluable is a set of set-up bearings. In the kit you get a selection of shims for the carrier and pinion gear and a set of honed bearings for a slip fit on the carrier. Insert the pinion gear in the case with a pressed on bearing (new or used). Start with the original shim pack on the pinion and add or subtract shims as needed. Assemble without the seal because you will be working up to the final setting. Bolt the new ring gear in place on the carrier (new bolts are a good idea) I start with the old shim pack on the carrier and adjust as necessary. This involves a LOT of trial and error. I am not an expert. Once you have established the proper pinion depth and backlash then you can press the new bearings on the carrier and pinion gear and assemble the rear. It is a lot easier to do this with the rear out of the car.

Or you can just take your ride to the local differential shop and pay the man
I have always had a lot more time than money and I am not afraid to get dirty.