Fire signs (Aries, Leo and Sagittarius):
They'd be on the streets. Maybe the leaders of a small disorganized resistance group. Their usual tactic is to blow things up. Probably looters. The alien's biggest pain in the ass.
Earth signs (Taurus, Virgo and Capricorn):
Leaders of the organized rebellion. Most committed to the cause and feel responsible for everyone under their command. They're digilent, no nonsense kind of leaders unlike the more flashy fire signs. Probably think too much before launching an attack. Their cautiousness is their downfall.
Water signs (Cancer, Scorpio and Pisces):
The YA protagonist. Just kidding, sort of. They may be on the streets, fending for themselves and protecting their loved ones. They're recluted by the rebellion and their belief in the cause is astounding. They won't see eye to eye with the leaders and might go solo after a while.
Air Signs (Gemini, Libra and Aquarius):
The undercover agents. They infiltrate the aliens to destroy things from the inside. Awed by the alien technology/culture, might be tempted to betray humanity and switch sides. Most likely to have their curiosity come back and bite them in the ass.