If you want to keep in touch with your friends, relatives or just post amazing photos of your trip, buy a local sim-card in Saint Petersburg. There are many operators – TELE2, Megafon (especially loved by tourists), Beeline etc. You can easily find one of their offices in the city center. Despite the fact that people working there are young it could be not that easy to find a person properly speaking English. Anyway, don’t get upset and keep searching! In any case, you can explain in layman’s terms what you need – internet, calls, messages.
When workers of an operator company will sell you a sim-card don’t get nervous if they ask your passport – it is the common procedure. Prices for services might be different and dependent on data size provided. For example, TELE2 offers a very cheap option – 5,5 rubles (less than 10 cents)/ per day for 100 Mb. If it is not enough you can buy a data package 500 Mb or 1 Gb, or even 5 Gb for price starting from 250 rubles. Keep in mind that Internet is quite cheap in Russia.