How do I decide which type of pronoun to use when I have multiple pronouns?

Many people become confused about which case to use when more than one pronoun is involved (example: she and I, him and me). Many students, believing that nominative pronouns sound more "correct," are reluctant to use objective pronouns in such situations. Try splitting the sentence into two parts to determine the correct case for the pronoun.
Example: She/Her and I/me went shopping.
She went shopping. I went shopping.
Her went shopping. Me went shopping.
Correct: She and I went shopping. (She and I are the subjects of the verb went; therefore they must be in the nominative case.)
Example: Miguel went to the movies with he/him and I/me.
Miguel went with he. Miguel went with I.
Miguel went with him. Miguel went with me.
Correct: Miguel went to the movies with him and me. (Him and me are the objects of the preposition with; therefore they must be in the objective case.)