Learn Finnish: Minä tykkään suomen kielestä.

This is because of the verb tykätä (to like). In Finnish, tykätä and pitää demand that the thing you like is in the elative case, which means adding the -sta/-stä ending. This rule is called verb rection.

Why is the word for Finnish written as suomen with an -n at the end?

Suomen is in the genitive case, meaning of Finland. The phrase suomen kieli literally translates to the language of Finland. Notice that even when kieli gets the -stä ending, suomen stays exactly the same as a fixed modifier.

How does the base word kieli become kielestä?

For many older Finnish words ending in -i, the final -i changes to an -e- when you add case endings. This makes the stem kiele-. Then you just add the elative ending -stä to match the verb tykkään.

Could I use pitää (to like) instead of tykätä in this sentence?

Absolutely! You could say Minä pidän suomen kielestä and it means exactly the same thing. Both verbs require the elative -sta/-stä ending. Tykkään is just a bit more relaxed and extremely common in everyday speech.