Just got my Apple Watch is there supposed to be a adapter for the usb to plug into

no, I don't think they've included ac chargers with the watchs in a long time

you can use an old ac charger with the right connector

or you can charge it by connecting it to a computer

or you can purchase a new ac charger

Power & Cables - Watch Accessories - Apple

Stands - Watch Accessories - Apple

Wireless Chargers - Watch Accessories - Apple

No, Only the cable (usb C to the magetic apple watch charger) is in the box. If you want to profit from fast charging you have to buy a seperate USB C wall adapter.