One way to tell if your curling iron can support dual voltage is to check for either a sticker or numbers printed on the handle, base or plug. This location might depend on the make or model of your curling iron and could also be written in the instruction manual or on the box.
Single voltage could say a specific number - such as 110V.
Single voltage might also have a small voltage range with a dash to accomodate small voltage fluctuations - such as 100-120V.
Dual voltage will say a large range separated with a slash or dash - such as 100/240V.