1- Stockholm to Helsinki by AirMany direct flights between Stockholm and Helsinki are operated by Scandinavian Airlines (SAS) and Finnair. They're also usually the cheapest flights available between these two cities, starting around $130/£80. The flights from Stockholm to Helsinki or from Helsinki to Stockholm depart several times a day and only are an hour long. Quick and easy, but not the cheapest way.
2- Stockholm to Helsinki by ShipIf you have some time to spare while traveling, there's a 16 hour long ferry connection between Stockholm and Helsinki leaving in the afternoon and arriving the following morning. The Viking Line and the Silja Line ferries both cover Stockholm-Helsinki (and Helsinki-Stockholm). Both cruise lines include on board services such as bars, restaurants, different types of cabins, and duty-free shopping.
The Viking Line offers cheaper cruise prices but uses older ships; Silja Line cruises are more expensive but also offer more elegance. Booking a weeknight cruise ticket from Stockholm to Helsinki is cheapest, and there's another discount if you buy a round-trip ticket.
Starting around €40, this is a cheap way to get from Stockholm to Helsinki or back, but not very fast. (You could also take a ferry from Stockholm to Åbo, Finland, and make your way south to Helsinki from there by bus or car.)