Learn Spanish (Latin America): Bata los huevos y añada la leche.

This is how formal commands work! To give an instruction using the polite usted form, regular -er and -ir verbs swap their usual ending for an -a. Since batir (to beat) and añadir (to add) are both -ir verbs, they become bata and añada. This formal tone is very common in written recipes.

How would this sentence change if I were giving the recipe to a close friend?

If you are talking to someone you know well, you use the informal tú command. For regular verbs, this form looks exactly like the normal present tense form for él or ella. So, the verbs keep their -e endings, making the sentence Bate los huevos y añade la leche.

Why is there no word for you in this sentence?

In Spanish commands, the subject pronoun like tú or usted is usually left out. The specific endings on the verbs bata and añada already tell the listener that they are the one being instructed to do something.

How do I know whether to use el or la for a word like leche?