Municipal buses (in Russian, the word to look for is "avtobus") and minibuses ("marshrutka") run between the airport and the Moskovskaya metro stop on Moskovsky prospekt. The commercial bus ride costs about 35R. If you're traveling with a tour package, all transfers will have been arranged. If you're traveling alone, you're strongly advised to make advance arrangements with your hotel. There are plenty of taxis available, but you'd be ill-advised to pick up a cab on your own if you don't speak Russian. Foreign tourists, especially passengers arriving at train stations and airports, are prime targets for scams, so be skeptical about offers.
If you want to take a cab, look for a desk with a "TAXI Pulkovo" sign at the airport exit. A clerk there will tell you the price you need to pay for your destination in the city. He or she will also give you two pieces of paper, one for you and one for a taxi driver, on which the price is stated. The driver won't be able to charge you more than that. As you exit the airport, look for a person in a reflective yellow vest, who will direct you to a vacant taxi. A taxi ride to the City Center will cost 700R–1,000R and take about 40 minutes. When you return to the airport, a regular cab that you order by phone will cost you between 750R and 1,250R.