First, you go to the emergency room. Tell the intake nurse that you are suicidal and you have a plan. You will be escorted very politely to a section of the ER or hospital. It won't take you too long to notice that this section is locked with guards and they will not allow you to leave. They won't let you keep whatever bag you came in with. Depending on where you live and what night it is, it is quite likely that you might see a few police officers, with people hand-cuffed to beds or hall railings. Some of these people will appear to be flat out insane. It will slowly come to you that you are in a locked ward with recently arrested criminals and that the rest of these patients don't seem all that rational either.
A nurse will come in to ask more questions and discreetly check you over for things like shoelaces or paper clips that you might use to slit your wrists. A doctor will come by eventually, (as in maybe within 4 to 6 hours), talk to you also with emphasis on whether you have a suicide plan, and run a drug screen. You will not be allowed to leave during this time.
Once the doctor determines that you are a clear and present danger to yourself or others, you will be admitted, even against your will. Where you go from there depends a whole lot on your health insurance and what beds are available. It is not unusual at all to find yourself being transferred to a different hospital. You will not be able to travel there yourself. EMT's, with police if necessary, will transport you.
Once at whatever hospital you end up at, assume that you will have a 3 day hold. (Unless you agree to check yourself in.) Regardless, if you have any kind of decent health insurance, you will be there for 7 days. Only 7 days, because that's all your health insurance is going to pay for. That's long enough to stabilize you on drugs and then kick you out.
In the mental ward, you can expect 3 meals plus snacks every day. In a good hospital, there might be art therapy and group therapy and random bizarre entertainment. Like AA meetings when you are not an alcoholic. Like some wannabe drill sergeant screaming at you to exercise. Like the craziest film you ever saw about how to find your happy place. That kind of entertainment.
Under no circumstances will you be allowed to just stay in your bed all day or maybe just read a book. No, no, you will have to socialize constantly with your fellow co-patients. Some of whom make no sense. The best of them have been arrested by the police for anger management issues or maybe they tried to rob a drug store. You will have serious doubts about the people who generally lead your groups, since most of them do not have any significant degree and seem to have fallen into this profession after they had significant substance abuse issues. If you are lucky, you will see your appointed psychiatrist maybe 2 hours a week. Then they will kick you out after doping you up on drugs. Nothing much will change in your life except now you have a label.
So sorry to be a downer, but you did ask the question. What happens after I go to the ER with suicidal ideation? In America this is what happens. I have had lots of unhappy clients and read lots of medical records and this is what happens. Unless your family is prepared to pay 10K a week out of pocket net, this is what you can expect.