Kurz und knapp short and sweet
Dresden at a glance
Short answer: Plan two days. Day one covers the old town: the Frauenkirche, the Zwinger, the Fürstenzug and the river terrace. Day two is for the Green Vault treasures, the Neustadt and maybe a Semperoper tour. Add a third day for Saxon Switzerland or Meissen. Book the Historic Green Vault ahead; it uses timed tickets.
Dresden was the seat of the Saxon electors and kings, and they filled it with palaces, art and treasure. Much of the old town was destroyed in February 1945. Since then it has been rebuilt piece by piece, and the Frauenkirche, reconsecrated in 2005, has become a symbol of reconciliation.
My tip: the old town is compact, so walk everything. Cross the Augustus Bridge to the Neustadt in the afternoon for a completely different Dresden: courtyards, street art and cafés.