You don't need to give them big words, for starters.
I read what's probably an unhealthy amount of fanfic. One of the trends I've noted is the whole smart people=big words thing, even when the character in question does not talk that way in canon. Notably, Twilight Sparkle from My Little Pony: Friendship is Magic.
As far as I can recall, almost every time Twilight appears, even if only for a few seconds, she
1. Learns something.
2. Teaches something.
3. Organizes something.
4. Tries to understand something.
5. Some combination of the above.
The show is remarkably consistent with this. Take "A Friend in Deed", where Twi shows up for about five minutes. She spends all of them reading a book or advising Pinkie Pie. That's 1, 2, and 4. These traits became even more important in Season 2, where Twilight became one of the main cast instead of the main character of the series. And since they couldn't resort to the old glasses+sweatervest=smart symbolism, they were forced to pay special attention to how they wrote Twi, especially since they couldn't have her busting out the big words on a show aimed mostly at kids. I can't really remember how Twilight was characterized in it, but Lilpip of "Fallout: Equestria" similarly shows herself to be a clever and resourceful protagonist by being clever and resourceful.
You know that gag where the smart person says something in technical language, and then the regular folks get others to explain it? MLP's used that gag exactly once
in two entire seasons. But fanfic has her using big words all the time.
There is a reason the pollysyllabic genius is rarely the/a primary protagonist. Even Holmes has Watson. One notable exception is Cryptonomicon
, which has two really smart guys, WW2 Cryptographer Lawrence Waterhouse and modern day computer guy Randy. Waterhouse is, as his dialogue, actions, and thought processes show, really smart. And more than a little eccentric. He doesn't talk quite the same way as everyone, but is still accessible. Even his contemporary, Marine Cpl. Bobby Shaftoe, is fairly smart himself. Randy is a 90s guy, and he talks just like everyone else unless it gets technical, and so, more or less, do his colleagues. Here's a sample of all three