Papertrail is great for this...you can of course setup syslog to route to a central server and just be logged in tmux / screen on that particular machine to read off the stream of logs (I prefer papertrail though + saved searches and hipchat "pings" when saved searches are matched on incoming events).

General devops / sysops/ sysadmin knowledge can be had through a variety of means - I got most of my knowledge from simply reading the FreeBSD manual and making a lot of mistakes with my own servers.