How do you actually ask your own manager for a raise without it being unbearably awkward?

I've been at my job a bit over a year, took on more than what I was hired for, and the market rate for my role has clearly moved. I know I should bring it up. I also freeze every time I imagine the conversation.

For people who've done this from the inside, not a new offer, just asking where you already are: how did you open it? Did you bring numbers, wait for review season, put it in writing first? Anything that made it less terrifying.