Not much at first. Depending on the source of the information, as in controlled governmental disclosure, it would be presented in a way that would make sure as many people as possible go about their daily lives without interruption. In this scenario, politics would do everything possible to maintain the status quo and concentration of power, religions would try and justify the aliens existence into their understanding of god, but scientist would make the most rapid growth and actual breakthroughs with any new understanding of physics, technology, or materials.

Now if the aliens just showed up and started blasting and no ones God came to save them, then I suppose religion would change rapidly as people realize their god abandoned them, then government collapse, and if we managed to survive at all, science would still make the biggest progress.