The act of acquiring free drinks whilst drunk. Much like minesweeping this may involve simply picking up leftover drinks or stealing but whereas minesweeping is often a last ditch effort from an out of pocket drunk digbying is considered more of a sport requiring cunning and ingeniuity from it's players.
Similar to a dickensian style pickpocket the average digby-er may use techniques such as distraction, persuasion and trickery to acquire their target drink.
garrath: you were on a digby session all night, god knows what you were drinking and you nearly got punched by some crazy scottish lady.
hayley: good night then?
paul: where did stacey get all those shots?
charlotte: she's digbying... she flashed her boobs at that stag do in exchange for sambuca.