Saint-Petersburg has well-developed transportation links to other Russian cities and large cities all over the world.

If you arrive by train:
There are several large railway stations ("vokzals") in St. Petersburg. Trains from Moscow, other Russian cities to the south and south-east of St. Petersburg and some trains from Ukraine arrive at the Moskovskii vokzal, linked to the metro station Ploshchad' Vosstaniya. Most trains from the west and south-west (including European countries) arrive at the Vitebskii vokzal (metro station Pushkinskaya). Trains from the east, nord-east, and nord-west (Helsinki) arrive at the Ladozhskii vokzal (metro station Ladozhskaya). Finlyandskii vokzal (metro station Ploshchad' Lenina) and Baltiiskii vokzal (metro station Baltiiskaya) serve only regional trains.

The railway timetables (in Russian) can be found here.

There is an online scheme of the St.-Petersburg metro lines (in Russian; external link). Ploshchad' Vosstaniya, Baltiiskaya, Ploshchad' Lenina, and Pushkinskaya stations are on the First (red) metro line; Ladozhskaya is on the Fourth (orange) line.

The Ioffe Institute is located at the corner of Politekhnicheskaya and Kurchatov streets, near metro station Politekhnicheskaya (First/red line), as shown in the scheme (you can click on it to enlarge).
Here you can see the facade of the Main building of the Ioffe institute:

If you arrive by plane:

Almost all passenger flights to St. Petersburg arrive at the Pulkovo international airport, located ca. 15 km south of St. Petersburg. Domestic and some international flights arrive at the Pulkovo-1 terminal, from where one can reach the Moskovskaya metro station by bus No. 39 or "route taxi" (express minibus) No. 39. Most of international flights arrive at the Pulkovo-2 terminal, from where one can reach the Moskovskaya metro station by bus No. 13 or "route taxi" No. 13. You have to pay something around 20 roubles inside the car.

From the Moskovskaya metro station please follow by the Second (blue) metro line to the correspondence station Tekhnologuicheskii institut (Technological Institute), then change to the First (red) line (see the metro scheme) and follow to Politekhnicheskaya.