The database server's message log is a record of all messages recorded by the database server. This is the first place to look if you have server problems, and a good place to check regularly.
This log will include messages that look something like the following:
2016-09-01 19:37:41 GMT [2507-1] LOG: database system was shut down at 2016-09-01 19:37:38 GMT
2016-09-01 19:37:41 GMT [2506-1] LOG: database system is ready to accept connections
We'll explain some more about these logs once we've located the files.