Scenario missions generally take 2-3 days for your followers to complete.  They do not guarantee player loot but has a higher chance than a Quest mission.  It is unclear if there is a limit on how many Scenarios your followers can complete each day, or if you are limited to an overall number of Scenarios per day.

It is believed that you need to have 3 followers per scenario, however it is unknown if these 3 followers must be a specific level to do a scenario mission.