Whether it's a new team cap or something you scored you got from that conference you went to that one time — it's yours and you want it to fit just right. You can speed up the breaking-in process by wearing it in the shower.
The best way to break in a cap is just wearing it, but that can take a while and you don't want to wait that long, right? Brett at The Art of Manliness suggests that hot water is the answer:
Take a hot shower in your ball cap and wear it until it dries. In lieu of the hot water soak, I've known guys to wear their baseball hat in a hot shower (heat and moisture!) and then just keep on wearing it until it dries.
You can also soak the cap in hot water, wait for it to cool some, and then wear it until it dries, but you might as well kill two birds with one shower. Now you can add your new, perfectly fitting cap to the rest of your tidily kept collection. Keep in mind, the hot water fitting process only works for wool or cotton caps. If your cap is made of polyester or similar materials, this won't work.
How to Break In a Fitted Baseball Hat [The Art of Manliness]