Simple answer is do not. The farther they are from you on the corporate tree, the bigger the no.
I have been a part of a few colleagues' end to the team. I hated doing it but one directly impacted my work (transferred), the other was requested upon me (fired), one that did absolutely no work (transferred), etc.
There is no good to snitch on someone especially if the boss does not bring it up. Boss bringing it up may be the only opening but even then tread very carefully. If you are unsure, then do not say anything negative. Feel free to omit positive but at worst stay neutral.
First Example
He was hired because he was a friend of a director. His career was a very non-technical role put into a role that required multiple technical roles. I did my job and trained him. I repeated multiple things to him. Things got ugly when he started "throwing me under the bus" by saying that I didn't train him.
Unfortunate for him, I had really good reputation by the time he joined so most of his attempts were met with a lot of question marks. I have worked with difficult colleagues before, so I started to use these strategies.
Keep records. I made sure that I always emailed everything to him. Even if it was a call, I will send a summary of the call, the decisions made, and the information he needed. Anytime he said he didn't know or said I didn't tell him, I would just respond to the email to remind him the information that I supposedly did not send. Near the end, I had resent the same email 5 - 10 times.
I basically did all his work. If he did work, I had to redo all of it and have to go through many people angry that that have to explain the work again. I can even tell him (when we are alone together) exactly where it was in his notebook.
Eventually, I just had enough of it. 1 month of training; 2 months of "re-training"; 2 months of supervising his work and correcting everything; 1 month of basically just doing his work. I basically just wrote to my boss and asked her to give me his work directly and exclude him completely. I explained I would save the company time and money if he just stayed home.
Her solution was that she will take over supervisory role of his work. I do not know what happened, but he was eventually transferred to another group. My boss was eventually let go couple months later although this may not be related to the guy. She was not very well-liked to begin with. I was the only one to send her off.
Second Example
The second person can talk the talk. He sounds very impressive after working with the company for a year after graduating. I suspect he was not well liked by the previous group and sent to us packaged like it was a great deal.
We were in the same line of work. I did not have to do the initial training or the second training. Supposedly he was not getting it correct and I was tasked to train him again. His work is full of errors: grammatical, data, format, etc. Each time I would point it out, he would thank me because he is such a perfectionist and cannot stand those things. There are quite a few things that I do not point out mostly due to the sheer amount of time that I spend just correcting the fundamental parts of his work.
I did not have a good impression of him. My boss kept assigning me to help with his work. I eventually documented all the time spent on his work. At this job, I was able to do my assignments within 3-5 days. It would take me 6-10 days to "help" him complete his.
This time, I spoke with my boss and said that I was no longer any help to him. I was spending more time fixing his work than just doing the work myself. My boss also took over primary supervisory role. Eventually, he was fired.
At some point he was put on probation then a second probation.
Sadly, he was not even fired for terribly poor quality work but he was snoring during one of the executive meetings.
Third Example
I had to train someone who used to do the same work. I later found out she used to work for our team before I was on the team. I also learned she was transferred out because no one wanted to work for her.
Yet somehow I had to train everything from the start. I would give her tasks with expected dead lines. She did not do them.
I simplified the tasks. One of these task would just be to create a template (copy, paste, then rename a file) which takes 5 - 10 minutes. I'll check the next day and it will still not be done. When I question her, she would say she will work on it. On the second day, she will say that she did not know how to do it. I would show her on that call, then explain she can do the rest. Third day, still nothing done and she does not even join the meeting. No show on fourth and fifth day. I reported the missed meetings to my boss because I was not sure she was on PTO which he said she was not. After a week, she has not even completed the first task and was not joining meetings.
At this point, the assignment is overdue so I just do the work. I give her a new assignment with the same tasks. This time I just do the work in a separate folder because I already expect her not to do the work. After another week of no progress, I just submitted my portion.
I have only reported to my boss that she has not shown up for most of her status meetings, does not even respond to emails or instant message, and has ignored most other things. I tell him just give me the assignment because I am just wasting time checking on her. I was also a contractor and I get paid the extra hours anyways.
Eventually, I learned that she was transferred. After another two years, I still saw her on the active directory.
Suggestion to Manager
In most cases, no one will ever jeopardize their reputation to snitch on someone else. I have talked to many colleagues who have complained about others. I can guarantee you that none of them will say a peep to a manager or HR. Anyone that snitches already have pretty bad personality, and no one wants to be lumped with them even if it is with good intentions.
I just happen to be confident in my work. I also make sure that I already have a good standing reputation. I am still very careful on what I share and who it is shared to. Everyone else have always just quit and did something else. Then you are just left with the crappy people who also just moved up a spot on the seniority ladder.
Why do I suggest others to just say no? Look how hard it is to fire someone. I cannot imagine providing any more evidence on how useless someone can be. #1 and #3 provided absolutely zero value. #2 at least did something even if it was still zero value. If anything I can argue that they provided negative value because I have to spend more time to correct the work. My team even got back an already known low-performing person.
Unfortunately, I have no way to prove that I am a pretty optimistic and patient person. I have given them lots of passes and liberties before I started my list on them. Technically, a list of CYA (or CMA in my case). Because no matter what, you always need to watch out for yourself. You never know when someone will push you under the bus. (Also doubles as a good source for yearly reviews)
If Any Action
If you do need to do something, my recommendation is to phrase the request as a detriment to your performance. I used to be able to do 20 tasks in a week; now I can only do 10 tasks a week due to addressing other tasks like training or assisting others. Or, I used to be able to complete a task in 2 weeks; now it takes me 4 weeks to complete. Or, I have been putting in overtime to cover these additional tasks that are not mine; I've worked overtime everyday for two weeks.
If manager does not do anything, make sure to track the changes. If management has issue with your decreased performance later, you need this list to back yourself up. If you get below expected year-end evaluation, this can prove that you have gone beyond expectations. If you leave work incomplete, this will also help back you up.
If management still has issue, do not invest more time in that company. Start looking elsewhere.
In more cases than not, having a detailed list will make you appear to have more leverage compared to someone that does not (assuming both people are on somewhat same level). I prefer to be more passive aggressive. Not to be a bad or evil person, but also as my "hidden" test for the manager if they understand some level of relationship intricacies. If they just want only hard evidence and facts, then I do not believe they are very fit managers. They clearly will not understand a good number of people.
