Learn Spanish (Latin America): Nos presentamos el uno al otro.

The pronoun nos can be reflexive (doing something to ourselves) or reciprocal (doing it to each other). By itself, Nos presentamos could mean "We introduced ourselves" to someone else in the room. Adding el uno al otro clears up any confusion, making it 100% clear that the action was reciprocal: we introduced each other.

Does el uno al otro change if the people involved are female?

Yes, it must agree with the gender of the people involved. If two women are introducing each other, they would say Nos presentamos la una a la otra. If it's a mixed group, or a group of men, you use the masculine form el uno al otro. If there are more than two people, it becomes plural: los unos a los otros.

Why is the word al used in the middle of this phrase?

Al is the mandatory contraction of a (to) and el (the). When people do actions to each other, Spanish often requires the "personal a" before the person receiving the action. So it literally means "the one to the other."

How do we know if presentamos means "we introduce" (present) or "we introduced" (past)?

For regular -ar verbs like presentar, the "we" form is exactly the same in both the present tense and the preterite (simple past) tense. You just have to use context to know which one is meant. Here, the English translation tells us it happened in the past.