Most items and equip with useful information have their realtime stats displayed in their tooltip when hovering over item icons in your inventory. Items will begin collecting stats when they are picked up. Survivors will have their damage skills tracked. Mousing over players in the scoreboard will show some character stats.
To reset the stats, right click or hold down the reset-spam key (defualt LCtrl) on the item, or press by default LCtrl+F5 to reset all stats, or enable the setting that resets stats when the item is lost. Change config ingame with either itemstatistics_reloadconfig or RiskOfOptions.
Host needs the mod for clients to see stats. There should be no issue if someone is missing the mod.
Modded survivors and skills will be automaticaly tracked if they properly fully implement RoR2's DamageSource.
After the end of a run, stats are outputted to the log.
For skills, Mult's second primary, Void Fiend's Corrupted Drown, and Chef skills boosted by Yes Chef will credit the special slot instead.
The numbers should be accurate and take into account proc chains and DoT damage.