My dog chewed up the corner of my kitchen cabinet and I need advice on how to fix it. The corner will have to be completely rebuilt and I'm not sure the best way to do this. We've got the typical builder grade cabinet base with a dark stain. Any suggestions are greatly appreciated.

Since they are typical builder grade cabinets, the least expensive fix that will make it as good as new will be to replace either the entire cabinet or the cabinet front. The hard part could be finding the manufacturer (depending on how old they are). Removing the cabinet could be a challenge but I'm guessing that it was an end cabinet to make it available for chewing.

While it is possible to replace just the one piece on the cabinet face edge this is a job for a skilled cabinetmaker type as there is no margin of error in a fix like this. Even then, finding a piece that will stain and finish the same will be next to impossible.

Got a picture?
Post one then start looking for a kennel on line.

Here's a side view of the damage.

And here's the front view.

Does not look that bad in that picture.
Light sanding, a coat of matching stain, some wipe on poly.

I have repaired worse too. I taped off surrounding good finish with painters tape and used a wood putty type filler (the kind that is colored close to wood tone but also is stain & paintable). Sand flat to the tape layer when cured, and use a matching gel stain or acrylic paints to match the cabinet. Light wipe on matching gloss or mask surrounding area and spray on lacquer to finish.

I'd put in a small screw that will be fully covered by the putty as an anchor so the corner stays on first time somebody bumps it with a vacuum.

if it had been chewed more, I'd use Bondo and cut a little bit into the veneer, then patch the veneer using Titebond II or III glue, and then stain and varnish to match.