I'm not clear on the ownership of practices but clearly there are costs associated with establishing and operating a practice (the office and its furnishing, the billing system (often computerized), the medical records system, durable equipment, nalpractice insurance, etc). Someone has to make the investment but I think that most new docs are invited to work for a practice with the possibility of "buying in" after they've established themselves.
Now in private practice, patients come to see you, you bill them and they (or their insurance company) pay you. You may sign contracts with insurance companies to accept what the company is willing to pay in exchange for being a "preferred provider". People covered by that insurance company will have a financial incentive to see a preferred provider and that will drive patients to your practice. The down side is that sometimes you'll feel that the insurance company is paying you too little and that can cause some consternation.
Lizzm makes the medical points, I can add a few items from a sibling who has their own private practice, and started it around 5-10 years ago. Their path was to finish training in the specialty, then work for mid-sized groups for around 5 years, and then after building up a clientele, to start a private practice. There are lending institutions/consulting groups that assist in all setup functions, from hardware to computer applications to office furniture to lending funds needed to do this.
A thought (from my professional experience) is how to get clients - there will likely be a fair amount of repeat clients over time for a field like FP, but initially there will probably be both marketing expenses and downtime, a pre-existing patient body would be helpful here, although many practices have "noncompete" type clauses that would limit a physician from bringing their clients with them.
Some specialties (i.e. plastic surgeons) market heavily, do a google search on plastic surgery & your city and check this out. Physicians in this type of specialty earn much more from a major cosmetic procedure than removing a mole, for example, and would not have the same type of "repeat business" that a family practitioner would likely enjoy.
A downpoint of private practice, in addition to malpractice and patient insurance issues, is that you're running a small business, and will have lots of issues outside medicine to deal with; some MDs/DOs would not enjoy this. You're the one who would need to ultimately hire & fire staff, discipline staff when they make mistakes, figure out how to handle workload when your office manager goes on maternity leave, etc.
