Learn Finnish: Poika pelaa peliä. - The boy is playing a game.

Pelata is a Type 4 verb. To find its stem, you drop the -ta and add an -a (based on vowel harmony). This gives the stem pelaa-. For the "he/she/it" form, you normally double the last vowel of the stem, but since pelaa- already ends in a double vowel, it just stays pelaa.

How would I say the negative, "The boy is not playing"?

You use the negative word ei (for "he/she") and the bare stem of the verb, which is pelaa. So you get: Poika ei pelaa. Notice that for this specific person, the verb looks exactly the same in both the positive and negative forms!

Why is the word for game "peliä" instead of just "peli"?

Peliä is in the partitive case. In Finnish, verbs that describe an ongoing, continuous action (like playing, reading, or watching) require their object to be in the partitive case because the action is currently happening and isn't "finished."

Does "pelaa" mean "plays" or "is playing"?

It means both! Finnish does not have a separate continuous tense like English does. You translate pelaa as "plays" or "is playing" based on whatever makes the most sense in the context.