Learn Spanish (Latin America): Ganamos el partido fácilmente.

To make an adverb (a word like "easily"), you add -mente to the feminine form of the adjective. Since fácil (easy) ends in a consonant, it is the same for both masculine and feminine. We just add -mente to get fácilmente. A special rule for -mente adverbs is that they keep the written accent mark if the original adjective had one!

I learned that "game" is juego. Why does this sentence use partido?

Juego is used for games in general, like board games or video games. However, when talking about a sports match or a sporting event (like a soccer or baseball game), you use the word partido.

Doesn't ganamos also mean "we won" in the past tense?

Exactly! For regular verbs ending in -ar (like ganar), the "we" form is spelled and pronounced the exact same way in both the present tense ("we win") and the past tense ("we won"). In real life, you figure out which tense is meant based on the context of the conversation.

Does the adverb fácilmente have to go at the very end of the sentence?

Not strictly, but it is the most natural spot here. Just like in English, you can often place adverbs that describe how you do something right after the verb or at the end of the phrase. Saying Ganamos fácilmente el partido is also perfectly fine.