I did this trip not even two weeks ago. Basically there are lots of companies/options for crossing from Helsinki to Tallinn.
The companies are SuperSeaCat, Linda Linne, Tallink, Silja, Nordic, and Viking.
There are "fast boats" which can make it in 90 minutes. Some of the slower ferries can take up to 3 hours. We were late to the port and had to grab the last 3 tickets they had - which were in business class on the Linda Line. Those were 38 euros each. A regular ticket was only 19 euros. But Linda Line is the cheapest because a regular ticket on a Silja fast ship was still 38 euros.
To make it more confusing, the prices change by day and even time. Its cheapest to go over to Tallinn at night I believe.
The best thing to do, if you're going to be in Helsinki for a day or two, is to stroll the Esplanade area (two streets of shopping with a park running between them, its a main part of town) and look for young people clad in all bright lime green clothes. They are roaming tourist information desks and carry the schedules and price list for all the fast ships/ferries. They were an incredible help to us.
Oh, and one last bit of advice, the 1.5 hour fast ship is a little bumpy - try not to be too hungover.