Okay, how on Earth does the Vertigo-verse (TheSandman + Spinoffs, Hellblazer, Swamp Thing, and The Books of Magic) tie in with the mainstream DCU? Characters appear back and forth between them — usually in the direction of DCU to Vertigo — and some have even made temporary or permanent jumps between the 'verses — Swamp Thing started out as a DCU character before becoming one of the flagship titles of Vertigo, and Animal Man and Doom Patrol spent time as Vertigo series before making the jump back to DCU. But the thing is that massive, world-changing events that affect the entire universe don't affect both equally — when Doctor Destiny or the Nameless Beast drive the entire world mad, no-one in the DCU notices, while you never see John Constantine or any of the Sandman ensemble commenting on things like the Infinite Crisis or Final Crisis.
You mean the John Constantine that first appeared (no, seriously) in an issue of Crisis on Infinite Earths?
a) He first appeared in Swamp Thing #37, one month earlier — and Swamp Thing was running a story at the time that was a tie-in to Crisis. b) Doesn't really answer my question. Besides this one-time thing, they don't really link up over huge events after that.
Blame Dream. He's the incarnation of stories, and thus, is the linchpin between the two publications. Superman doesn't age, but Constantine does, and yet they occupy the same universe with the same timeline? While this shouldn't be possible, the story itself allows for it because of Dream, who's existed longer than physics.
Short answer: it doesn't. The Vertigo titles have stopped being in-continuity with the DCU. Hell, some of them have stopped being in-continuity with each other. (As for the same characters appearing in both places... well, its DC comics, they have a multiverse and Elseworlds and such things.) See the Headscratchers page for the DCU for more discussion on that.