There's a lot of really good advice on this thread and I just wanted to add a little about my experience since starting my private practice in 2017, because the type of practice I have seems a little different from what other people are describing they do so I wanted to share just another option of how you could design and structure your ideal practice.
I have a cash pay, concierge/"high touch" psychiatry private practice. I am in Los Angeles, which is a large, urban area but I mentor a group of early career psychiatrists starting private practice and there are people with similar successful practices in Iowa, Indiana, Wisconsin, Nevada, etc, so geography is NOT a limitation for setting up this kind of practice.
I practice integrative psychiatry, which is NOT alternative psychiatry or homeopathy - it's standard of care psychiatry with "extras," and a way of thinking about the patient from a holistic, relationship-oriented perspective. I do functional evaluations and integrate low-risk evidence-informed complementary approaches into my treatment plans, like mind-body practices, nutraceuticals, dietary interventions, and of course psychotherapy.
What I do is not for everybody, so the kind of practice I describe may or may not resonate with you. I can say though that I absolutely love what I do and I'm happy every day I get to do it. I was never going to be someone happy in a regular job like a community setting or academic center or HMO system like Kaiser. I'm a control freak and an entrepreneur and heart and there's nothing better to me than having total autonomy to create my dream practice exactly as I want it.
First things first: f you want to have a successful private practice WITHOUT accepting insurance the first thing you need to understand is that if you are not clear on what differentiates you from other psychiatrists, there is no real reason why a patient will pick YOU to see as opposed to someone else. If you are just like any old psychiatrist, then growing your practice will be a haphazard process of who randomly stumbles upon you via referral or psychology today or whatever, as opposed to people actively seeking you out.
You will essentially be a commodity (although a highly trained one), which means that patients will see you as interchangeable with any other psychiatrist and will therefore shop based on who is cheapest/has the worst boundaries/will just prescribe them Xanax or whatever.The more you communicate what makes you unique on your website or when communicating with patients, the more the "right" kind of patients for you will self-select into your practice.
There are certain ducks you need to get in a row before starting your practice (I reviewed my recommended software solutions for starting a private practice in this thread:
What EMR to use in solo private practice?) but the biggest mistake I see early career psychiatrists make is trying to be too perfect right out of the gate. The limiting factor to filling your practice will almost certainly NOT be your clinical skills (although you should always grow your clinical skills) or the fact that you haven't yet incorporated or written the perfect office policies or opened your business bank account.
It will be that you don't know enough about marketing. In the beginning, your main focus should be getting patients in the door and mastering some basic marketing fundamentals.
Someone asked here about social media/online marketing or potentially hiring ad ad agency. I don't think this is necessary. I filled my entire practice though 1) Psychology Today, 2) referral sources, and 3) Google ads. Now I get patients mostly through organic search traffic, but those first 3 things are how I built my practice initially.
Honestly, if you really master those 3 marketing strategies you will fill your practice. Look at your competition on Psychology Today in your geographic area and write a better profile than them (it shouldn't be that hard - avoid jargon and speak the language your patients speak). For referral sources, don't limit yourself to therapists or PCPs, think bigger -- where are your ideal patients hanging out, and what services do they use? Do they see functional MDs, go to hot yoga, go to acupuncturists? Do they go to gyms, hire personal trainers, see massage therapists? Put yourself in the shoes of your ideal patient and imagine where they go and see if you can find them there.
If you are considering paid ads, you really, really need to understand the concept of return on investment/ROI. I teach people how to do Google ads and inevitably everyone starts and puts in $100 and then freaks out when they don't have a patient yet and then they quit. That's WAY too soon to give up. There is a learning curve with paid ads and but once you get it down it's like a spigot you can turn on/off to get patients. On the other side, people will throw away thousands monthly on an ad agency and not get a single patient. As long as you are making more money off the patients you see than you are spending on ads, you are in good shape.
Social media is useful not because you will find patients that way (think about it-- social media is international, where are you are probably licensed only in one or maybe a few states). Social media is useful because after a patient hears your name (say via a referral source) they will Google you (when's the last time you used a service provider without Googling them first??). So if you have social media posts/videos/blog posts/etc available it will be more data that patients can use to learn more about you and decide to see you as opposed to someone else. I often have potential new patients tell me they decided before even talking to me that they wanted to see me just because of something they read on my website or social media that resonated with them.
This brings me to my next point, which is, if you have a med management only practice (without doing psychotherapy) it will take you FOREVER to fill and you will need 500+ patients to have a full practice. If you do therapy, you can have a full practice with 50-100 patients. I love it because I can be a "one stop shop" for my patients -- I don't just tweak their meds and send them on their way, I work with them in a comprehensive way to improve their lives. So if you are remotely comfortable, consider adding psychotherapy services to your practice. Even if you aren't comfortable, get some additional supervision/training and learn as you go.
I hope this helps!