Read books written in first person to learn how to do it well. I suggest anything written before 1970. Recent stuff can be good, but it's rare. Old School writers tended to be better educated and better read. There, I said it.
Bolded mine, and I would politely disagree. There's plenty of wonderful first-person contemporary fiction to love and learn from, here's just a handful of my favourites:
How the Light Gets In - MJ Hyland
The Hundred Secret Senses - Amy Tan
Extremely Loud and Incredibly Close - Jonathan Safran Foer
Never Let Me Go - Kazuo Ishiguro
The House of Stairs - Barbara Vine
Chocolat - Joanne Harris
Gone Girl - Gillian Flynn
We Are All Completely Beside Ourselves - Karen Joy Fowler
The Paper House - Anna Spargo-Ryan
The Blind Assassin - Margaret Atwood
Cat's Eye - Margaret Atwood
May We Be Forgiven - AM Holmes
Anything by Marian Keyes
Sue Grafton's Alphabet series