How do I use EPOLLHUP
You use EPOLLRDHUP to detect peer shutdown, not EPOLLHUP (which signals an unexpected close of the socket, i.e. usually an internal error).
Using it is really simple, just "or" the flag with any other flags that you are giving to epoll_ctl. So, for example instead of EPOLLIN write EPOLLIN|EPOLLRDHUP.
After epoll_wait, do an if(my_event.events & EPOLLRDHUP) followed by whatever you want to do if the other side closed the connection (you'll probably want to close the socket).
Note that getting a "zero bytes read" result when reading from a socket also means that the other end has shut down the connection, so you should always check for that too, to avoid nasty surprises (the FIN might arrive after you have woken up from EPOLLIN but before you call read, if you are in ET mode, you'll not get another notification).