Wow, a generic error handling mechanism for the whole project.
On the good side, your manager probably realized that error handling, because it happens everywhere, is probably not tightly coupled to any other part of the project. In this way, it is easier to give to a young developer who isn't seeing the big picture very clearly yet.
On the rather more difficult side, error handling is a topic for mature coders. I know my own thinking about error handling has gone through several phases in a long career. Questions like return codes vs exceptions, localization of error messages, error recovery strategies, are all very sophisticated topics that a new developer has no hope of mastering.
You may discover that your boss really meant something vastly simpler than you think, like "Write a set of functions for copying error message text to a log file," or "Set up a couple of header files with ranges of error constants for different classes of errors." This you can probably do easily. If your boss really meant develop a whole strategy for handling errors, they get credit for thinking of the idea, but no credit for handing this important task to a new guy.
But bosses want what they want, and there's maybe nothing you can do but try to give it to them. In that case, google is your friend. You can google "error handling", "error reporting", "error reporting in C#", "error printer", and related terms and find out what packages other people have put together. Looking at the list of features of several error logging packages and asking yourself why this feature was choses will allow you to reverse-engineer a list of requirements. Seeing how different people solved the same problem might give you a sense of which implementation ideas were best, so you can recommend or code up a specific solution. This is going to get you about halfway to your goal, providing an error printing or logging facility. Having produced *something*, you may be able to fall back on "Well, I've only been doing this for three months, what did you expect?" Otherwise, I think that defining overall how the whole app will handle and recover from errors is a discussion that the whole team will have to participate in. It's extremely naive to think one person can define it. (Nevertheless, I once had a boss who was angry at me because I could not poof this problem out of existence for him.)