I imagine it will take eons. Based on the information available to me, the universe was formed by a large explosion due to the collision of two random atoms no larger than a pinhead. At current time, the explosion is still happening, hence, the universe still expanding. But it's eventually going to reach an apex where it can no longer expand, and the only two events that could happen after that would be dissipation, or retraction. Dissipation would be a slow and almost unnoticeable event, likely just the dying of the stars littered across the universe. Retraction seem like it would be the quickest way for the universe to end (while still taking many many millennia), but would be ultimately more violent, with everything inside the universe returning to its point of origin. Meaning lots of asteroids and comets crashing into Earth, and the annihilation of the human race happening well before we see the outcome. Just my thoughts on the subject, though.