How would God curse someone?

Well, an entire chapter of the Qur'an is Allah cursing Muhammad's uncle (and his wife):

Surah Al-Masadd
In the name of Allah, the Beneficent, the Merciful

The power of Abu Lahab will perish, and he will perish. (1) His wealth and gains will not exempt him. (2) He will be plunged in flaming Fire, (3) And his wife, the wood-carrier, (4) Will have upon her neck a halter of palm-fibre. (5)

Since you were wondering, there you have it! Merciful and compassionate indeed :-)