Swap the plug. You've got a very high probability of success with no further action. If the bulb doesn't light or is too dim swap it too but in most cases a European 240v rated incandescent, halogen, or LED bulb will have no issues on US 110v. Rarely, LEDs might not light at all and the others could be dim. So, if you're unlucky you'll need to swap the bulb too.

When going the other direction, US to Europe you need to be a little more careful since running at too high of voltage could pose a fire risk so checking the bulb rating would be prudent. The majority of bulbs are tolerant of the full global voltage range though, it's a lightbulb, not sophisticated equipment.