As an object, use “my friend and me” (that is, use it in the same places you would use “me” alone). For example, “Make sure you call my friend and me.”

As for the order of the words, contrary to some of the answers above, **both are grammatically correct**. You can say “I and my friend” or “my friend and I” and follow rules of grammar either way. The reason English teachers insist on the latter is because of *style* rather than grammar. It’s considered to be more of a polite style to mention your friend before yourself. However, doing so doesn’t change the meaning of the sentence, so there’s nothing grammatical about it.

The convention is to put oneself second in pairs, last in lists. The basis of the convention is that to do otherwise is unseemly and forward, lacking in good breeding. Like many “grammar rules,” it’s done that way because it has always been done that way.

It is just proper english.

For example, say this sentence out loud and try to determine which one sounds better:

1) I and my friend went to the park yesterday.

2)My friend and I went to the park yesterday.

Sounds better and I think you should always refer to yourself last.

it’s the grammar rule.

My friend and I went to the store.

The store sent the package to my friend and me.