You can reach Finland by land (well, not really), sea, or air.
Air:
From the US of A, you can find flights from the usual places:
Kayak is one of my faves. Orbitz and cheap tickets can also yield some deals.
If you want to flounder about the old world before or after the wedding:
Air Berlin is a cheap way to get back to civilization, which flies from Helsinki to Dusseldorf. From Dusseldorf, you can get just about anywhere on the plane, train or otherwise.
Also occasionally viable is Ryanair, which is wont to "sell" free tickets. Stings attached include bus rides to and from remote airports. The remote airport in Finland is outside of Tampere, which will cost you about 2 hours and 20 euros (per head) to reach from Helsinki. This should be your last option.
Land:
Also an idea to kick around is seeing the old world via steam power. The Eurail ticket is a good deal if you would like to take the train around the continent. If you're traveling by rail, you'll probably need to get a boat to Finland...
Sea:
There are boats that run to Helsinki from Stockholm and Tallinn, among other places.
