Learn Spanish (Latin America): Pela el tomate, por favor.

Because this is a command (giving a direct instruction). To tell someone you address as tú (informal "you") to do something, you take the normal tú form of the verb, which is pelas, and simply drop the final "s".

Wait, doesn't pela usually mean "he or she peels"?

Yes, it does! The informal tú command form looks exactly the same as the normal present tense form for él/ella (he/she). You can tell this is a command because of the context: you are speaking directly to someone to give an instruction, made even clearer by adding por favor.

How would I say this formally, using the usted form?

To give a formal command to someone you address as usted, regular -ar verbs like pelar (to peel) swap their ending vowel to an "e". You would say Pele el tomate, por favor.

How do I know to use el before tomate?

Tomate is a masculine noun, so it takes the masculine word for "the", which is el. Because Spanish nouns ending in "e" can be either masculine or feminine, it is always a great idea to memorize the el or la right along with the new word!