From Stockholm you can take the boat, Viking Line (
www.vikingline.fi) or Silja Line (
www.siljaline.fi), to Helsinki. The cheapest tickets with the smallest cabin are a bit more than 20 euro (Viking Line is normally a bit cheaper than Silja line), but it also depends on when you´re travelling, etc. The trip takes the whole evening and night (you´ll be in Helsinki the next morning), ´cause usually the purpose is to have a party on boat ( = to drink and eat well, listen to the (also live) music, dance, sing karaoke, etc.)...
From Helsinki you can take the train to St. Petersburg:
www.vr.fi. The cheapest tickets cost about 50 euro, but by bus it´s of course cheaper (then it´s maybe better to google for the cheapest prices).
Hopefully this helped at least a bit. (=