Staraya Ladoga is small enough that everything of interest is reachable on foot. The fortress, the St. Nicholas Monastery to its north, the Assumption Monastery to the south, and the burial mounds out in the fields are all within roughly two kilometres of each other. A relaxed circuit covering all of them takes two to three hours, with time spent at each site.
There is no public transport within the village. If you arrive by bus or marshrutka from Saint Petersburg or Volkhov, you will be dropped on the main road and can walk from there. If you need a taxi — for instance to get back to Volkhov for a train connection — local drivers are available, or ask at the fortress café or museum.