Learn Italian: Aspettiamo dieci minuti. - We are waiting ten minutes.

In Italian, the regular present tense covers both actions happening right now ("we are waiting") and general habits ("we wait"). You usually just use the simple present verb to express either one!

Shouldn't there be a word for "for" before the ten minutes?

You can say per dieci minuti (for ten minutes), but Italians very often drop the per when talking about how long something takes. It is exactly like in English when we say "We are waiting ten minutes" instead of "waiting FOR ten minutes".

Where is the word for "we" in this sentence?

The ending of the verb tells you who is doing the action. The -iamo ending on aspettiamo always means "we" (noi). In Italian, you usually leave the subject pronoun out unless you want to add special emphasis.

If I want to say "It is ten past three" on the clock, do I also use the word minuti?

Usually, no! When telling time on the clock, Italians just say the hour and the number, like sono le tre e dieci (literally: they are the three and ten). You mostly use the word minuti when talking about an amount of time passing, just like in this sentence.