Learn Spanish (Latin America): Mi perro no puede correr rápido.

This sentence uses the structure poder plus an infinitive. When you combine poder with another verb to say what someone can do, only poder gets conjugated. Since puede already tells us who is doing the action, the second verb, correr, stays in its full, unchanged dictionary form.

The verb is poder, so why is it spelled puede here?

Poder is a stem-changing verb. This means the vowels in the middle of the word change when you conjugate it. For most subjects, the o changes to ue. Since mi perro counts as a third-person singular subject (like he or it), poder becomes puede.

Why does no go before the verb? In English we say "cannot" or "can not".

In Spanish, to make a sentence negative, you must put the word no directly before the conjugated verb. You cannot put it after the verb or attach it to the end like we do in English. So, "cannot" translates to no puede.

Can rápido mean "fast" as well as "quick"?

Yes! Although rápido is typically an adjective meaning "quick", it is very commonly used as an adverb to mean "fast" in everyday Spanish. This works exactly like English, where we say "run fast" instead of "run fastly".