Getting around Sevastopol, on a day to day basis, is much like getting around many Ukrainian cities -- by foot, by mini-bus marshrutka, and by city bus. Given the hilly terrain and circuitous routes created as Sevastopol grew around its bays and shoreline, walking is less likely to be efficient, especially after one leaves the city center.
Note that English maps and schedules for buses do not appear available based on internet searching and that one may need to depend on the word of citizens, operators, and fellow passengers to find the right route and stop. Buses and marshrutkas are economical, though often crowded, with marshrutkas being faster and slightly more expensive. Some travel sites e.g., virtualtourist.com contain comments recommending boats/skiffs that will take tourists to beaches and islands. Note that its much harder to get off boats if you realize you are on the wrong one and it is also difficult to leave a dicey location if the only transport is by boat.
Good road maps of the town with street names in both Latin and Cyrillic characters cost 7.5UAH from press kiosks.