I'd like to preface this by saying that there's no one real good way to know, because everyone is going to display the symptoms differently. Also that I've been there - I have tried to kill myself three times in my life so I am writing from personal experience as well.
That being said, there are several signs to look out for. Suicide often goes hand in hand with depression, so knowing the signs of depression can be a big help. Things such as pulling away from loved ones, no longer being interested in things they once enjoyed, changes in sleeping habits (sleeping too much or not enough), changes to eating habits (over eating or starving ones self) and general behavioral changes are some really big signs.
Self-harming is a sign that someone might be suicidal. Not all people cut their arms/wrists, I did it on my inner thighs to avoid drawing attention and getting in trouble with my mother. And not all self-harm is cutting; intentionally starving, taking drugs to induce vomiting to help to that end, taking drugs in general (both legal and illegal) and other things that are damaging to the mind and brain and hopefully lead to their deaths as a passive suicide.
I remember a depression thing I saw once that also said giving away personal possessions is a sign of being suicidal. While I never did this, I've known some people who have. So if the person you're worried about is suddenly giving away things they loved and prized at some point in time that's also a sign.
But perhaps more importantly than the signs is that by asking a question of this sort I imagine you're worried about someone close to you. So reach out to them, encourage them to get help. Look up suicide hotlines, and what to do if you think someone is suicidal. Check in with them often, let them know that you care. If they stop responding and you're worried they may have done something call the emergency line and tell them. More often than not they'll send someone to check and make sure, and if you're lucky your area has a mental health facility the person can stay at to get help for little or no cost to get the help they need.