I'm really new at this but I'm a big fan of the Japanese language. I found a list on Quizlet with the most used vocabulary such as to go, to see, etc to learn with their Kanji (I already learned Kana). My question is since there's always a Kunyomi and/or Onyomi pronunciation, which one am I learning right now? For example, いく （行く）= to go (this is how Quizlet teaches it). Is いく one way of saying to go or is there like a basic pronunciation or does it depend on the word?
Kanji change pronunciation based on many factors, and one kanji can have a dozen different prounciations. It's not productive to worry about all them, and instead you should learn complete words.
The same kanji can represent different words with different readings, like 行(ぎょう)-line and 行(こう)-act, in which case the reading and the meaning should be clear from the context. Sometimes, the author of the text will provide furigana (the reading of the word, written in hiragana, positioned on top of the kanji) to specify which reading and meaning is intended.
And in some cases, words can have the same readings but their meanings differ based on the pitch accent. Something to be aware of when listening to native speech.
To answer your question 行く (いく) you learned is the kunyomi reading, and yes sometimes there are more kunyomi readings and sometimes more onyomi readings for a kanji.
Almost always when you have kanji together they use onyomi instead, like the word action for example, 行動 (こうどう) you use the onyomi of 行 (コウ) and 動 (ドウ). To be clear here I wrote the onyomi readings with katakana.
So I guess in the beginning when you learn words like 帰る、行く、食べる、飲む。they will all use kunyomi, then when things get more kanji heavy you will use the onyomi more frequently.