Her and me went to the store
Mom gave money to she and I.
There is an incredibly easy way to remember which pronoun(s) to use in a plural situation such as the ones above. Here's the cheat:
Her went to the store. Me went to the store.
Mom gave the money to she. Mom gave the money to I.
These are obviously not right when said apart and neither are they when put together. Instead, think of the right way to say them apart, then use those pronouns to put them back together in the plural, like this:
She went to the store. I went to the store. Therefore, She and I went to the store.
Mom gave the money to her. Mom gave the money to me. Therefore, Mom gave the money to her and me.