The old town of Chioggia is small and entirely walkable — from the Duomo at the southern end to Sant'Andrea at the north is about a kilometre along the Corso del Popolo, with everything of interest within a few minutes of that spine.
To reach Sottomarina, walk over the long road bridge (about 20 minutes from the southern end of the corso) or take one of the frequent local buses that run from the corso to the beachfront. A small foot ferry crosses to the eastern side of the canal near the Ponte Vigo. Bicycles can be rented near the bus terminal and are useful for the longer reaches of the Sottomarina beach and for the lagoon-side cycle path.