If you decide to travel by plain or train whatever country you come from it’s important to arrive at Moscow or Saint-Petersburg first. Then (from Moscow or Saint-Petersburg) the more comfortable way to reach Petrozavodsk is by train.
Trains departing from Moscow:
All the trains depart from the Leningradsky railway station
Trains departing from Saint-Petersburg:
All the trains depart from the Ladozhsky railway station