International airport Pulkovo (LED) accepts a lot of international flights from many European countries every day. You can take a look on that on the airport website
You can come to the city from airport by city bus #39 for 0,5 Euro per person and 15 minutes to the nearest subway station. This bus accepts PayPass / PayWave (don't expect other buses to accept it). You can also use PayPass / PayWave to enter subway stations. For other public transporation, prepare Russian cash or buy special card ("podorozhnik") at subway station.
You can also use Uber to rent a taxi. UberX is cheap enough (like 5 euros across half city, 2 euros for short distances), and has fixed rates from/to airport (up to 15 euros to Blincom site). Please take into account that most of drivers even don't understand English (but you don't need talk to them, just type in your destination). Never
use random (even "official") taxi from/to airport, that can be very expensive.
For flights we recommend you to look on some discounters like AirBaltic
. You can also arrive to Helsinki or Tallinn and travel to St Petersburg by bus Lux Express
(cheap and comfy solution) or high-speed train Allegro