Purchase a plug adaptor if you don't have one already. European plug adaptors look like a U.S. socket on their front face and have rounded prongs extending from the other. If you plan to travel to other locations, you can alternative buy a "universal" adaptor, good for use with any type of socket.
Insert your curling iron's plug into the adaptor. Devices such as curling irons are only intended for use at voltages common in their country of sale, so inserting the plug into the adapter will not only allow you to plug it into the wall, but also prevent it from shorting out.
Plug the adaptor into the wall socket. Wait a few minutes for your curling iron to heat up, keeping an eye on the rate at which the temperature increases. Although the adaptor will lessen the current that flows into the curling iron itself, it might not be down to exactly 110 volts. As such, your curling iron may take in more voltage than it normally would, in which case you should avoid using the maximum heat setting.