Planning a low budget and environment friendly trip to Iceland from Helsinki, Finland next summer for me and my friend. Haven't been able to find relevant information on possibility for cargo travel (from where - eg. Norway, Denmark? - timetables, prices etc). Expected departure from Helsinki around June 18th, return at latest on July 7th 2015. I'm very thankful for any related advice (and first time on stackexchange, so apologies if I didn't formulate my question in a best possible way)
I don't know if boarding a freighter by asking around in the port or approaching the ship's captain is still possible nowadays, many things I read suggest it is not. In a large port like Rotterdam, there is also no way to get anywhere near most ships without a car and some credentials.
On the other hand, there are many opportunities to travel on a freighter through an agency but this is not particularly cheap. I have also never heard of a ship linking Finland and Iceland directly (although it seems possible I guess). Answers to Where can I get information on freighter travel? and What is the cheapest available freighter voyage anywhere? provide a lot of info on these agencies and some typical trips but you will need to approach one of them with your needs to see what's possible or not.
One problem for your specific plan is that many ships in the Baltic sea travel between ports in Poland, Denmark, Finland, Sweden, Russia, etc. and the biggest European seaports in Germany, the Netherlands or Belgium. Cargo bound for farther destinations can then be transferred to bigger ships there. The feeder container ships serving the Baltic are specifically designed for the dimensions of the Nord-Ostsee-Kanal in Germany and probably don't venture elsewhere very often (it's not economical to use a smaller ship than possible on a given route).
With two different ships, it could still be possible to book a trip to Iceland entirely by sea but you would have to include a stay in Rotterdam (probably for several days/weeks as you need to wait for the right ship and can't rely on cargo ships' schedules to ensure a smooth connection). To give you just one example of what you can expect price-wise, here is a round-trip between Anterwerpen and Finland for about €800 per person and here is a round-trip between Rotterdam and Iceland with another agency for a bit more than €1000.
You would need to find ships allowing one-way passages instead of round-trips, which should be cheaper, but I would guess that the total could be around €1000-1500 per head, (much) more expensive than flying (as of writing I see Helsinki-Reykjavik flights in May for about €120 one-way). Going to Norway or Rotterdam by train/ferry/bus as suggested by David in a comment could save some money but the crossing to Iceland itself would likely cost around €500 in any case.
Finally, if you want to avoid flying for the sake of the environment and are willing to give up the freighter travel aspect, there are ferries between Iceland and the continent. I am not sure about the price, but it's probably cheaper than a freighter.