What is a sentence in first person?

Person as used here is a quality of verbs. A sentence may contain verbs in the first person, or any person. The 'persons' are ways of expressing how things in the world relate to the 'self'. Every living individual is the 'self' from her or his own perspective. Self reference is the First Person; I dance, I write, we dance, we write. The Second Person is reference to another person who is with me or who I am addressing even if not present; you dance, you write. The Third Person is indirect reference to another person on thing; he dances, she dances, it dances, they dance. Sentences do not have to have verbs in one person only.

Example: [all first person] I should have taken my umbrella with me when I left for work this morning.

Example: The last time we communicated, [first] you shared [second] your wonderful news about the puppy; it was growing [third] by leaps and bounds, and was boundlessly joyful.

You will not always see the Words I, you he, we, she, it or they, as signals of the 'person' of a verb. [all third person verbs] From Oscar Wilde: "Murder is always a mistake. One should never do anything that one cannot talk about after dinner."