There is a Taxi dispatch desk in the arrivals hall of the international terminal. They offer a fixed fee service to a given address. In February 2013 it was 900 roubles to Bolshaya Morskaya 11. You can pay at the desk by credit card or the taxi by cash. By far the cheapest service (apart from the bus & metro).
Ruble notes are not normally stocked by currency exchanges outside Russia, so you will typically arrive with no rubles. If you are happy with an ‘airport’ rate there is a currency desk in baggage area of the international terminal. Even better in the arrival/meeting area there are ATM/Cash machines which work with most bank cards. If you are comfortable with cash you will get even better rates from the local currency exchange business (they are always run by a bank). If you are arriving by train from Finland a good currency exchange service will pass through the train at the border.
There is a lot of walking in St. Petersburg, so save your legs by trying to get used to using the bus & metro early in your visit. There are three kinds of buses in the city: regular buses, trolley buses (electric) & route taxis (older, smaller, normally the bus number is prefixed by a K eg K3).
The buses, trolley buses & trams currently ( May 2015) cost 28 roubles for a single journey. There is always a conductor, try to have close to the right money.
The metro is 31 roubles to anywhere in the city. They are planning on introducing zones someday.
The metro operates using token coins (jetons), if you have 100 rouble notes you can use an orange automatic machine or newer ATM type machine, otherwise use the ticket window (just show how many you need with fingers). There are 5 metro lines, numbered & colour coded. Stations with 2 lines intersecting confusingly have two names. The nearest station is Admiralteyskaya only 50 metres/yards from the apartment on the side street.
If you happen to be using public transport with a suitcase expect to pay a baggage fee normally the same as a regular ticket.
Don’t be shy of stepping on any bus or trolleybus plying Nevsky prospect as they nearly always go the whole length (except trolleybus 17). You can study bus routes using maps.google.com – click on More & then Transit.