How Do You Refer to Yourself and Someone Else?

We are taught that it is rude to put yourself before someone else, and that you should say I. I (and we, he, she, you and they) are pronouns. They are used to represent a person instead of using their name. These pronouns are classed as subject pronouns

subject pronouns

In English, the subject pronouns are I, you, thou, he, she, it, one, we, ye, they, who and what. With the exception of you, it, one and what, and in informal speech who, the object pronouns are different: i.e. me, thee, him, her, us, you (objective case of ye), them and whom (see English personal pronouns).

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as they do the action of the sentence.

How do you refer to yourself and someone else in a sentence?

The traditionally correct sentence is "Larry and I had a meeting today". To know whether to use the nominative case ("I") or accusative ("me"), remove "Larry": you'd say "I had a meeting", not "Me had a meeting". These days, especially in informal usage, "Larry and me had a meeting today" is also common.

Is it correct to say yourself and John?

No, the phrase “myself and John” is absolutely incorrect. Especially when we are talking about the person speaking as a subject, the use of myself as their personal pronoun is nothing but a false choice.