That’s a bit of an open question! Until the re-release of BB we would have played LRB6 (Living Rulebook 6) which is a complete and stable rulespack freely available on the internet.
Cyanide’s first Blood Bowl game used these rules so you might already be familiar with them.
Their Blood Bowl 2 game had some rule changes that so far only exist in that game. Off the top of my head this was limited to giving the Human catcher armour 8 (from 7 in LRB6), changing the way money was spent before a match and making skills mandatory to use (i.e. you couldn’t choose not to use a skill in some corner cases). In short, you’re coming from Blood Bowl 2 then LRB6 should be very familiar.
BB2016 is the latest official ruleset from Games Workshop but that is a bit of a moving target currently. It would be hard to point you towards a single resource as the rules are drawn from the new boxset, two expansions, two erratta, an online pdf detailing team races and a number of White Dwarf articles. GW have recently released an Almanac for $50 which is supposed to pull most of these together but I haven’t checked how exhaustive it is.
For the most part I feel that BB2016 is a collection of extra rules with few substantive changes to the LRB6 ruleset.
If you wanted some bedtime reading I would start with LRB6, not least because it’s free, but if you’re coming from a PC background you probably know most of it anyway. The main learning curve coming from the computer game is things like moving you turn marker and tracking which of you players have acted.