Though it's true that identical twins have the same DNA, that doesn't mean that there's no way to tell them apart. First of all, identical twins do not have identical fingerprints.
This is because fingerprints aren't determined only by your genes. Identical twins normally have very similar fingerprints, but pressure in the womb and contact with amniotic fluid can influence the ridges along fingerprint patterns.
Basically, even though identical twins have the same genes, the environment can cause small differences in appearance.