Learn Spanish (Latin America): Ayer organizamos un club nuevo.

Yes, it does! For regular -ar (and -ir) verbs, the nosotros (we) form is exactly the same in both the present tense and the preterite (completed past) tense. You have to rely on context clues to know when it means "we organize" versus "we organized". Here, the word ayer (yesterday) makes it perfectly clear that this action happened in the past.

Why isn't the word nosotros (we) used in this sentence?

In Spanish, you can usually leave out subject pronouns like nosotros because the verb ending (-amos) already tells us exactly who did the action. You only need to include nosotros if you want to add special emphasis or clear up a genuine confusion.

Why is it club nuevo instead of nuevo club?

In Spanish, descriptive adjectives like nuevo (new) almost always go after the noun they are describing. So, instead of saying "a new club", you say un club nuevo (literally "a club new").

Is the word club pronounced exactly like it is in English?

Not quite! Even though it is a word borrowed from English, it has been adapted to Spanish pronunciation rules. The "u" makes an "oo" sound (like in the English word "flute"), so it sounds more like "kloob". Also, to make it plural, you add -es, making it clubes.