What are the cheapest trains from Helsinki to Saint Petersburg?

I know you want to travel by train, but if price is a concern, you really should know that minibuses are much cheaper: €15-25 vs €65+ for the train. Details for schedules, boarding points etc on Wikivoyage.

And if you're willing to compromise, you could try taking a bus to Vyborg (Viipuri) just across the border, and then a cheap domestic Russian train (182 rubles, c. €4) the rest of the way. The international expresses to St. Pete also stop off in Vyborg, so you could change trains there, but this won't save you much.

The booking of tickets is rather strange. If you book from Helsinki you will need to do this via Finnish Railways, if you're doing this from Russia you will need to do this via RZD. And depending on date, time and class tickets fluctuate between 65 Euro to 165 Euro.

Allegro Train (SPb Finlyandskiy) would be the fastest option.

Lev Tolstoi (SPb Ladozhskiy) train will be the cheapest one.

As @Karlson answered the question using information for current times, I want to add the information for futher trains. Technically this is not a direct trains from Helsinki to Saint-Petersburg, but there are plans of RZD to develop some general non-highspeed trains on regular basis.

The Federal Passenger Company and the Government of Karelia plan to develop further railway links with Finland. Work is now underway to organise regular passenger services between Petrozavodsk to Oulu, Imatra and Helsinki.

It is planned that during the first phase of implementing the project tourist trains will provide services will be formed at the request of tour operators. The next train between Petrozavodsk and Joensuu is scheduled to run by March 8.

In the future, the Federal Passenger Company may begin regular passenger services 3-5 times a week if passenger demand is sufficient.

Among the prerequisites for the further development of international rail traffic with Finland is to improve the facilities at the border crossing point.

And another one:

Cross-border services between Russia and Finland were substantially improved in December 2010 with the launch of Allegro tilting trains between Helsinki and St Petersburg. Under a co-operation agreement signed in Petrozavodsk on September 25, RZD, Finnish national railway VR Group and local authorities in both countries are now examining other potential passenger routes, including Petrozavodsk – Oulu and St Petersburg – Imatra.

So I think that from 2015 year you can add some extreme part and travel by regular trains, and not in high-speed Allegros.