I'm in the extremely early stages of a wedding (pre-engagement early). I like to plan things ahead of time.
I've never been to a non-religious wedding. What is said for the wedding part? That is what I'm trying to figure out.
All I know is the Bible related stuff with a priest or preacher.
I've thought about potentially asking law/political science/sociology friends to officiate the wedding, but I'm afraid of them being in the same boat as me.
Andy, kudos to you for doing your research with plenty of time to spare. The joy of a secular wedding ceremony is that pretty much anything goes! The pain of a secular wedding ceremony is that all that freedom can be overwhelming. Some couples who have traditional religious ceremonies decide to do so not because they're especially religious but because, well, following a ceremony template is way, WAY easier.
(To clarify, I'm ALL for couples having Bible-based ceremonies … if the folks getting married are practicing Christians. But I think it's disrespectful to smile and nod your way through a religious service you don't actually believe in, so I vote for secular couples going for secular ceremonies.)
That said, I've got lots of ideas for you. First, take a look at my archive of guidance posts about ceremonies. You'll find everything from vows referencing zombies to how to build a ceremony for a shy couple, to ideas for great secular readings to include in your service. If you read only one post, make it this one: Wedding Ceremony 101: Crafting your own wedding ceremonies from scratch.
I've recently featured several modern ceremony components like unity candles, unity cocktails, sand ceremonies, and ring warmings. Between Offbeat Bride and the rest of the web, there are a bazillion secular ceremony ideas out there, and no shortage of books!
Perhaps the best advice, however, is to find a truly great officiant/celebrant who can help you with this process. I've featured several celebrants and officiant stories on Offbeat Bride, and you might get some inspiration there. A good officiant will be the perfect combo of thoughtful adviser, skilled writer, and excellent public speaker. Don't be afraid to ask around with your law/political science/sociology friends — you may be surprised to find that some of them are already internet ordained and have helped with other friends' weddings!
Also, be sure to check out our post on how to write your own ceremony: Wedding Ceremony 101