Holy, my recommendation is to contact the priest/church directly, as each church's protocol will be slightly different.
I've mostly attended "regular" funerals (held in a funeral home), but I've also been to some Episcopalian church funerals and Catholic church funerals. All in all, other than length and religious formality, there weren't too many differences between them all.
Catholic funerals include a Mass service with Communion, which catches some people off guard. They also include Holy Water and Incense Burning, which can surprise those not familiar with the Catholic church. Usually the printed funeral program will indicate when to kneel, when to stand, when to pray, etc.
Here are some websites that might give you an idea of what to expect, but my best suggestion is to call the church directly, explain that you are not Catholic but have been asked to participate in the funeral service, and ask what they think would be helpful for you to know. (I wouldn't be surprised if they don't already have a "What to Expect" handout prepared that they can give you.) Also, ask to be seated with your girlfriend at the funeral itself; that way you'll have someone familiar with Mass who can help guide you in what to do when.
Our Lady of Grace - Catholic Church Encino - Burials
Catholic Cemeteries Chicago/Christian Burial Rites
Archdiocese of Los Angeles
GUIDELINES FOR CATHOLIC FUNERAL RITES-PDF
Archdiocese of Vancouver - Planned Giving
Policy on the place of Funeral Masses
Catholic Funeral: FacingBereavement
Catholic Funeral