Even though most Champions League matches are broadcasted on TV channels that you need to pay for, it is still a fact that UEFA wants some matches to be shown on free TV channels, to get more viewers and to get more sponsor money.
That is why you will be able to watch one match a week for free from the Champions League online also in 2015-16, because YLE will show it on TV, something meaning that you as a viewer can follow it for free both from your couch in front of the TV, or watch it online on your laptop, computer, tablet or mobile device. It is easy to watch YLE in Finland live online, and you can read more about watching it online here.
So, this is a brilliant way to watch the Champions League on Finnish TV. You should however be prepared for the fact that you will probably not understand to much, because the Finnish language is impossible to understand, and if you would consider learning the language it is even worse as it is considered to be one of the hardest languages in the world, and if you get through the trouble of learning it what makes it even more terrible is that it is not like any other language in the world, so it does not share similarities to other languages. That is why I personally would skip learning the Finnish language and probably watch the Premier League online on some other channel (if I did not know Finnish), and if I was to learn a new language it would probably be a more international language which would help me learn other languages easier as well.
Anyway, have fun watching Champions League on YLE in Finland!