The approach... in a word, minimal. Working with a limited track count forces you to make creative decisions at the time of the performance, which gives music a more human feel. Recording to tape makes it more difficult (but not impossible) to punch-in and fix small mistakes, and once you record over something it's gone forever. That means you have to be certain that you're capable of doing better than what's already recorded. There's a commitment involved that has become unconventional in today's world of Digital Audio Workstations with endless undo's and cut/copy/pastes. When executed correctly, the final product from working with analog tape is a more deliberate piece of art.
All that being said, I'm not a total purist. I try to record as much to tape as possible, but the method that works best in most scenarios is to record the initial 8 tracks to tape and then dump to digital and overdub in the box. No two projects are exactly alike and no one method works universally. The key is to figure out what the song calls for and make your best decisions based on that.
The following are a few examples of things I've engineered or produced at my home studio: