I am a PGY-IV planning on private practice and have looked into your question. I agree with Shikima that things are extremely variable, but to break down into more specifics I think it depends on whether you are in:
-solo private practice
-small group private practice
-a large organization like Kaiser or a community hospital (which is 'private' as opposed to academic)
Within at least the first two the number of insurances you take (if any) also plays a significant role.
For solo: you will likely have a mix of patients who come to you for medication management (standard times could be from 20-30 mins, though some solo cash docs I have met do one hour med management visits which occur at less frequency than therapy would). You can also opt for integrated psychotherapy and medication management, though with insurance this may not reimburse as well and you may need to lean more heavily on cash pay patients to sustain a therapy-heavy practice, or choose the insurance with the most workable reimbursement options.
For a small group: you may work very similarly to how you would in a solo practice with the group taking a chunk of your billing in exchange for administrative/office/coverage etc assistance. You may also utilize that infrastructure (secretary, billing, more formal office setting) to see higher volumes of patients, often times with insurances. You can probably panel on more insurances and see more patients in this model, referring to therapists as appropriate (or choosing to keep them for therapy yourself as you wish).
For a large organization: I don't know enough to say. It sounds like you would take a "team leader" role in many of these settings handling diagnosis, medication management, referrals to other providers, oversight of psychotherapy and general disease course, etc.
You would also likely sprinkle in various other interests like consulting, supervising, speaking, researching, part-time work (moonlighting, ER, forensic, etc), and plenty of other options as desired and available.
