Him/her - he she. It can be a possessive pronoun as in The ball is his. It can also be an object pronoun. Mary is going with her.
Her and I went shoe shopping. This is incorrect. The pronoun should be she. I hope you wouldn't say Me or Us went shoe shopping. Yes, Cookie Monster does, but in places other than Sesame Street we shouldn't. So the correct pronoun would be she.
The order of the pronouns also needs to be watched. It's proper to put yourself as the last in a combination. It's polite to do this. Jane and I rather that I and Jane. Another way I see this incorrectly used is Me and Jane went shoe shopping. Not only is the order wrong but so is the pronoun, unless you are Cookie Monster.
So, I guess the easiest way I've found to figure out the correct pronoun in a combination is to say it as if it's just me. I am going shoe shopping. If I works then use he or she. If it doesn't use him or her.
For a good easy site for grammar issues is: http://www.grammarbook.com
I hope this helps as you are writing to clear up some confusion about pronouns when more than one is used. Would you like a cookie?
Sophie Dawson is an author of Christian fiction. She has published three Historical Christian fiction novels; Healing Love, Lord's Love and Giving Love. They comprise the Cottonwood Series and are available on Amazon, Smashwords and other online retailers. Healing Love won best Religious Fiction in Authorstand.com's 2012 contest. She is currently working on two novels for the new Stones Creek Series and one contemporary novel. She hopes to have all three released by the end of summer 2013.
Sophie lives on the family farm with her husband and cat. The mother of two grown and gone (yes! fist pump) sons and has the cutest granddaughter that ever lived. She loves reading, gardening and has done just about every kind of needlework.