what to do

Ideally, you'll pick up on a patient feeling depressed, acting oddly, or making statements about death or wanting to harm oneself. Then you could intervene to provide for safety & a safe environment.

Exact protocols for patients who have demonstrated self-harm vary from facility to facility but you can bet that that patient will need very close monitoring (most likely one-to-one), removal of all risky objects like knives, strings and anything toxic and ingestable and evaluation by social workers or similar professionals. Restraints may be necessary.

I highly suggest you look up what to do in the policy and procedure manual now and not after you are confronted with this situation. It'll help you help your patients. :)

Also, be aware that policy and procedure manuals may be vague or even conflict with state or federal laws regarding restraints, seclusion and other similar measures. You may mean to protect patients from themselves but cross legal boundaries in the process. I've seen a few facilities with very squishy written policies about restraints which has led to confusion about whether a patient should be restrained or not. It's best to look up your state's nurse practice act too.