My artesian well just ran dry. Do I just wait for it to fill up?
The short answer is, depending on the source of the water table, it should fill back up over time. 
But there are many reasons, other than you leaving the hose on for a day, why your well can run dry.
Are there any new building developments in the area? 
Is your region suffering from low rain or snow fall this year?
Or, if there's excessive rain/snowfall, your well could have filled up with excess silt, effectively clogging your well pump.