We have three boys, but we sort-of used the same process for choosing each name (including our intended should-we-have-a-girl names).
We verbally hashed out favorites (easy enough).
We wrote out our favorites, sometimes on note cards (this is what I did, at least, and shared them with him) and on the back wrote the origin and meaning (and personal meaning, such as family member it was from or character in a book, etc.).
We put first names together with possible middle names and our last name to see how they look, sound, and what the initials would be.
We were both allowed "absolutely not"s, but the other was allowed a bit of pushing if done nicely.
When it came to the girl name we tried to pick (again, never needed it) we each had a favorite the other could not stand. Well, I liked his girl name, but not to name a daughter (Ophelia, really??? Yes, it's pretty, but the only literary context is Hamlet and she goes mad and drowns!). He did not like Deidre at all, even though I wanted to use his mother's middle name with it (sooooo pretty that way!). We were not getting anywhere, so we decided to start brainstorming girl names but we agreed to treat those two names as if they were not options at all. We started joking about a Welsh Arthurian text we read in college because it is full crazy names and, of course, that ended up being where we found our favorite girl name.
So, maybe start browsing online at names, look at things that you both like (books or films or historical figures?), write some down with the meaning (seriously, that can affect how you look at a name--I really liked Cecily but decided I didn't want to give a daughter a name that means blind, even if it is pretty), and play with them. I like looking at them, so write out middle names, your last name, and play name games for a while, even include some names you're not crazy about. You can search online for names by what they mean or where they're from, too, if you want something with a specific meaning. (Example, if you like something that means "light," you could consider Elaine, Ileana, Laneah, Ora, Areli, etc.)
It's early, so you have time to play with it. :)
(Oh, and I also liked the idea of using either of my grandmother's names--Virginia and Helen--and was given a definitive "NO!" I still think they're pretty, but not worth a fight!)