I've only had brief inpatient stays (on the order of days to weeks), so this is with that in mind:

-Don't assume I'm not self-aware. I can be very rationally aware of how irrational my emotions are. Help me by talking to the rational side of me about managing those emotions, rather than assuming that I don't even realize they're irrational

-Put yourself in my shoes. The last time I was on a psych watch in the ER and I was being forced to hand over all my possessions I was told that I couldn't even keep my bra under the hospital gown. When I was unhappy about this (not throwing a tantrum, just less than thrilled), the nurse, in an attempt to make me feel better, made some comment about how she loves being able to get home at the end of the day and take her bra off. I had to point out to her that there was a big difference between choosing to relax in your own home vs already feeling vulnerable and exposed and having your agency taken away, and to imagine how not even being allowed to keep your bra would further add to those feelings and the humiliation. She hadn't imagined what it might feel like to be going through before I said that (she was a nurse in an ER, not on a psych ward, and she was just the one they stuck with babysitting me)

-ask me. It's okay to ask what or what would be helpful at that moment. The answer might even be different at different times. It can be helpful to offer choices rather than expecting someone to know exactly what they need, e.g. "Would you rather I stay with you right now, or would you rather have some time to yourself?" "Would you like a hug, or would you prefer not to be touched right now?"
Making this choice also helps the person feel more in control at a time when they probably feel like they're having their control taken away from them. It's also a sign that you respect us enough to ask. If it were someone who wasn't hospitalized/in a care facility, you probably wouldn't presume to know what they needed without giving them a choice.
You can also ask before or after someone is distressed, if they're unable to tell you in the moment. Like "if you get upset like that again, what can I do to help?"

-Don't treat me like a child. You're seeing me at the worst possible moment. I'm sure you wouldn't want us to treat you based on your lowest moments in life. In my "real life" I function as an independent adult. Depending on how long you'd been out of school, I could have been your TA. If you assume that I have less life experience than you do or that I am naive and childish, it will show. It's not easy to set aside my pride and accept help, and it's a lot harder if I feel the need to defend my pride because the other person doesn't seem to respect me.

-You don't have to be completely serious all the time. It's depressing enough to be there as it is. It's a lot easier if you appreciate humor when we try to use it. It doesn't mean you're not taking our issues seriously if you laugh at our joke.

-The relationship we have when I'm not distressed will be the biggest factor in how helpful you can be to me when I'm distressed. If I feel like you don't respect me or there's no connection whatsoever between us when I'm not distressed, I'm not going to be at all receptive to you when I am distressed. If I really like you and I feel like we connect well and you understand and are trying to help me, then I'll generally find you trying to be supportive when I'm distressed helpful, even if the same words or behavior from someone else would have upset me more.