Compound pronouns involve a pronoun and a noun or another pronoun.
Unlike nouns, the case of pronouns changes based on their function. This is especially confusing with compound pronouns. For example, in the following sentences, the case of the pronoun "I" changes to "me":

Jim and I sat with her.
Jim and me sat with her.
She sat with Jim and I.
She sat with Jim and me.

To determine which is correct, remove all parts of the compound except the pronoun in question, then read back the sentence to make sure it is still correct. Let's try this on the first pair of example sentences:

I sat with her.
Me sat with her.

"Me sat with her" is clearly wrong, and "I sat with her" is correct. Now let's check the second pair of sentences:

She sat with I.
She sat with me.

The correct case is "me," not "I."