Several ways to do this, some more complicated than others. What I did here is fairly simple:
1. Enter your text on a new layer. Rasterize the layer.
2. I added a bevel & emboss to the text, but this is optional.
3. Select Edit>Transform>Warp>Arc, which bends the text into a smooth arc. You can adjust the settings to change the amount of bend. It's trial-and-error, but I used negative 10% horizontal bend.
4. Select Edit>Transform>Rotate to rotate the text to match the hat. Use the Move tool to position the text. You may need to adjust the size (Edit>Transform>Scale) of the text to match the available space on the hat.
5. I made some minor tweaks using the Warp tool and Edit>Transform>Skew.
6. Lastly, I used a Curves adjustment (with a mask) to lighten the letters on the right, matching the light shining on the hat.