Learn Italian: Siamo in ritardo, dobbiamo finire velocemente.

It is formed by taking the adjective veloce (fast/quick) and adding the suffix -mente (the Italian equivalent of the English "-ly"). Because veloce ends in an -e, you do not need to change it to a feminine form first; you just add -mente directly to the adjective.

Why do we say siamo in ritardo instead of siamo tardi?

In English, "late" is an adjective, but Italian expresses this state with the phrase essere in ritardo (literally, "to be in delay"). The word tardi is an adverb used to describe the time itself, like in è tardi (it is late). When talking about people being late for an event or deadline, always use essere in ritardo.

Why doesn't the verb finire match the "we" subject like siamo and dobbiamo?

Because it comes right after dobbiamo (we must). Dovere (must/to have to) is a modal verb. Just like in English, the main action that follows it stays in the infinitive form (the dictionary form ending in -are, -ere, or -ire). So you use the conjugated helper verb plus the infinitive: dobbiamo finire.

Could I put velocemente before finire?