Yes. You need a visa, but taking a train from Helsinki to St. Petersburg is completely simple. It's worth it too. St. P. is one of the strangest and most magical cities in the world. Try to do it during white nights, that is, within a couple of weeks plus or minus of June 22. Besides St. P., there are a lot of interesting places not far from Helsinki, Novgorod, Pskov, and even Moscow (which is less than 4 hours on the bullet train).
Russian trains are excellent but expensive; about $150 one way second class St. Petersburg-Moscow on the "Sapsan" bullet train. Flying is cheaper but a lot more hassle.
If I were you, however, I wouldn't go from Helsinki. I would sail right into St. Petersburg. It is a hassle, but a lot more fun, and definitely an adventure which would be worth it. The yacht clubs are extremely friendly and will help you fight the bureaucracy. It will be an adventure. Just follow the rules with extreme scrupulousness, make sure you've got someone in the Central River Yacht Club advocating for you, and you should be fine.
Noonsite: St Petersburg