I'll tell you what happened based on my experiences in a few mental hospitals (keep in mind, this is in the US, I have health insurance, and I am over 18 yrs of age):
1) First time I went to the ER was because I was wanting to kill myself. I walked in and they got my information, checked my blood pressure, I was scanned with a metal detector wand to make sure I had nothing dangerous on me, and then they took me back to a big room with multiple beds and a nurses station. They make you change into clothes that are basically just like paper towels. I had a nurse come ask me what was going on, and I explained. Then the nurse tried to give me a lecture I've heard 6000 times. They ask you basic background information, etc. Then a registrar came and got my insurance information. Then, a mental health assessor came and had me go into more depth about what was going on. She asked me if I was willing to be admitted. I said no (I had a bad image in my mind of what a mental hospital was and that scared me), so they did not admit me. They gave me resources about finding a psychiatrist, and both inpatient and outpatient groups. This whole process took between 4-5 hours. I did not have to pay at the hospital, but they did send me a bill for $200, which is the ER copay on my insurance. They did not contact anyone because I did not ask them to.
2) Second time, I admitted myself into an actual dedicated psych facility for those with mental health/addiction/etc issues. I had called before going so I knew what to expect. It is an acute facility meaning the average stay is usually 3-7 days. They tell you to bring a bag of clothes and toiletries, so that's what I did. They search through everything you bring, and make sure none of it is potentially harmful, such as clothing with strings, etc. I did share a room with 1 other girl and shared a bathroom with 3 other girls. It was overall a good experience. They had an activity room where I spent most of my time, doing puzzles, crosswords, watching TV, and they had group therapy multiple times a day. They also had more relateable people, atleast for me. In the ER, the people that are in the psych facility tend to be very...intense. Anyways, in this facility you see a psychiatrist every day for a small amount of time, they ask if you need any medications, and basically..whatever you ask for, you get (within reason). After 3 1/2 days I was discharged with the same resources the ER gave me. I received bills in the mail for both the psychiatrist and the facility itself (around $1000). We were allowed to call people using their phones however during group sessions the phones were turned off. They did have visiting hours but it was only 45 minutes a day. You let them know who you want this information released to (like your primary care, your parents, etc)
3) I overdosed on pills and was brought to the same ER I went to before. The police created an affidavit saying that I could not leave voluntarily for at least 3 days. The next day after I got out of the ICU, they took me to the psych part of the hospital. I was there for 5 days. I only met with the psychiatrist on 3 of the days. There were groups but they were not very helpful. The people there were very scary. People would always be yelling. I shared a room with a woman who had overdosed on heroin and had been throwing up constantly. You had to wear the clothes they gave you, again basically paper towels. The food was awful. The nurses will come around when your medication is due and will give it to you. They had visiting hours every day that were nice (4-10pm) so I had people come visit me then. I was so happy to be discharged. It was honestly one of the worst experiences of my life. There was nothing therapeutic about a psych ward at a general hospital. I'm waiting on the bill for this one still.
I would recommend, if you're going to admit yourself, do it at a hospital dedicated to mental health.
I'm sure I missed some things so if you have any questions feel free to ask and I'll answer