Unfortunately it is not possible to arrive to the campsite with public transportation since the place is a little remote. However, Kliffa will provide transportation to the campsite from Helsinki on the day the camp starts.
Most cities in Finland have a well-functioning public transportation system. If you want to explore Helsinki or another city a little bit more, it is usually cheapest to buy a day-ticket. You can always pay with cash, some long-distance buses also accept cards (not Visa Electron or MasterCard Maestro).
Public transport info, prices, timetables and more:
Helsinki area: https://www.hsl.fi/en
Hämeenlinna (a close city to Kliffa): http://www.hameenlinna.fi/Kaupunki-info/english/Public-transport/
If you want to travel between cities, check out these: