Death of a relative, break up... Sometimes personal things such as these occurs.
I think that personal life should be kept away from work. But sometimes, since we are human beings such events do impact our efficiency at work.
Should I tell my boss when I encounter such problems and that I may be less efficient at work because of this for some time? If yes, is there an appropriate way? Should I tell coworkers as well?
You should tell your boss, for example "my grandmother died yesterday". Your behaviour will change (not laughing about jokes that you would usually laugh about), and people can adjust their behaviour a bit.
I wouldn't mention performance problems in that context at all. Your boss may not notice anything. Or they may notice some change and keep your mourning in mind (knowing that this will stop). No need to draw attention to it and make them watch out for problems.
There may be company cultures where talking about personal issues is looked at as a sign of weakness, and if you work in a place like that you might want to keep quiet.
However, based on personal experience, I would say that talking helps. My wife suffered from complications from surgery last year, was in a coma for two months and is now permanently disabled. Caring for her would be a full time job by itself, and I have to do it in addition to my day job. Also of course this affects me psychologically.
I have been quite upfront with all of this with both my superiors and colleagues, since this rather affects my performance. And while I still have (obviously) to do the job I was hired for the company has been looking for ways to accommodate my situation, and my colleagues now at least understand why I'm constantly looking tired and show some understanding. Had I kept quiet that would not have happened.
So I'd say mention it at least - at the worst nothing will come off it, but maybe somebody is willing and able to assist you with your situation (but remember that other people have a life, also, so don't take it as an excuse to talk constantly about your issue).
It all depends on the kind of problem and the mental stamina of a person. I knew one colleague who was normal with all of us and it was only a decade later that I came to know about an extremely rough phase which he went through and most importantly something which none of us could ever imagine. I was taken aback by the way he handled the situation. He didn't let it impact his professional life; not even an iota of it.
Again, there was another colleague who could never work properly owing to his low lever of expertise; He was mourning someone's death and/but everyone gave him a benefit of doubt for that low output that he was giving at office.
Some people take advantage of their situation and some would never let it impact their professional life. It varies from case to case. It is important for you to assess the gravity of the situation, decide if you need assistance from your colleagues or will you be able to manage it on your own.
I am of the disposition that has found that keeping such things secret can be much more harmful than discussing it openly. That is my personal bias.
However, you have to judge what is the norm in your workplace, the personality of your boss, and the potential for the event to impact your performance.
For instance, I have relatives I have not seen or spoken to in years. If one of them were to die, I would be sad but it would be something I could easily compartmentalize and not have it affect work. So no need to discuss. That certainly was not the case when my beloved died after 26 years together. I cried at work every day for a year, so it was impossible to hide.
Even the worst boss is also a human being. Almost everyone will understand why the death of a child or a spouse would drastically affect you. Further, If you have brought such things up, you can get bereavement leave and you are more likely to get allowances for any immediate performance problems. People will likely ease your workload for at least the first couple of months. (Incidentally if your boss is one would would not be understanding of such things, that is a huge red flag that this is a very bad place to work, everyone has personal problems eventually.)
Most bosses prefer to know if there is a potential problem, so they can rearrange task assignments, deadlines or whatever might be affected. It is pretty much essential if you are going to take bereavement leave or use your personal vacation time to deal with a situation. It is the professional thing to do to tell them. You can (and should if you value your privacy) ask them not to tell anyone else about it except possibly others like HR would might need to know if there is an accommodation to make. Ask him to talk to you before he talks to any of these other parties.
A benefit of telling such information is that people will reach out to support you in any decent workplace. Co-workers will offer to help with your work load, people will tell you about how they coped through similar times, people may organize food for you or offer to drive you to places you need to go to etc.
The only time I have seen it generate bad feelings when someone told us about a personal issue was when the person was in control of when the thing happened and chose the worst possible time. (She chose to leave her husband the week before a huge deadline and left us stranded with her work undone. And well, frankly, she wasn't well liked either because she was having an affair with the CEO which led to the divorce.)
But when people let us know the issue, people tended to rally round and help.
Sometimes people don't tell and then use it as an excuse after they are reprimanded for poor performance. That, too, does not go over well. If you are going to have performance issues or see that you have started to have performance issues, talk to your boss as soon as you can. People can;t make accommodations when they don't know they need to.
Also be aware that no business can accommodate forever. You have to try to get yourself together as soon as you can.
There are also some things you probably do not want to tell or at least don't want to make a big deal out of. People have been fired for having some diseases like AIDS. Drug abuse is also something that is likely not going to be looked on as a good thing. Expecting performance accommodations for your hangovers is another. A breakup is less likely to get an accommodation than the death of a child. You might be able to take a day or two off, but no one is going to let you mope for weeks and have that not affect your performance evaluation.
No one cares that your pet fish died or you have a flat tire. Telling all the minor things that have gone wrong and treating them like they are major is not a good thing for your career. It makes you look like someone who can't handle ordinary life. People will see you as someone trying to get out of work if you think your flat tire should give you a pass that day for concentrating once you get to work. (Yes this is a real-life example.)
You also ask if there is an appropriate way to tell someone. If the death or event happened when you were not at work and you need to take the next work day off, then use the same channels you would to call in sick. In today's world that is often an email. If, however you are at work when you find out and co-located with your boss, then go tell them in person. If your boss in in another physical location then use the phone by preference and email as second choice.
Telling coworkers is another consideration. If they are going to be asked to take up the slack for you, it is probably best to tell them in general terms. You can just say you are having a personal problem or that you have been diagnosed with a medical issue but do not want to discuss the details. Or you can ask your boss to tell them what you want them told. As a minimum, they need to know you are dealing with a personal problem if it is going to affect there workload.
If you want to keeps things fairly quiet, you can tell people who you consider to be friends if you think they will maintain your secret.
