Short answer: Nothing. Nothing happens to humans under a red sun. We would find our visual capacity reduced since we developed under a white/yellow sun. And depending on where the star's habitable zone was, we might be a bit cold if it's a red dwarf or a bit hot if its a red giant. Other than that, the radiant energy of a star does nothing for human beings as we know them.
Detailed Answer: Humans unlike native Kryptonians are not physically adapted to live on heavy gravity worlds such as Krypton, nor are we genetically designed for superhuman abilities under the radiation of non-red stars. Superman's powers are likely not a side-effect of evolution, but of genetic engineering.
Humans moved to worlds with stars of different colors would garner no particular benefit, and depending on the nature of the planet could find ourselves in distress if the world was under a hotter and more energetic blue star whose radiation levels would be lethal to us.
To note the DCU's history, there have been stories in the 60's (during the Pre-Crisis Superman Era) that doubled the superpowers of Superman and gave humans superhuman powers under a blue star but those stories were likely the result of lack of scientific knowledge on the part of the writers. Humans would have no such superhuman adaptations or modifications to give us superhuman abilities.
Under a red sun, if the planet we were on was within the habitable zone around the star, we would be fine, although our visual capacity would be reduced. If the planet is not within the habitable zone we would be cold and unhappy.
A brown dwarf is a star that has not achieved luminescence. It emits more radiation to the environment than it absorbs from its parent star. Superman's energy stores would likely not be affected by the lesser radiation profile of a brown dwarf as long as there was another more powerful solar source in the area. Humans would need protection from the radiation of a brown dwarf if we were too close to it (say on one of its nearby moons) otherwise it would only be a threat if we were close to it. Jupiter and Saturn both possess some of the qualities of a brown dwarf. They are often called failed or sub-brown dwarfs. Both lack sufficient mass to make the classification. A gas giant with 13 times the mass of Jupiter meets the basic qualifications to be a true brown dwarf.
And as with so many things, the DCnU has not officially denoted what happens to humans under blue stars. But the proper answer, without extraordinary circumstances should be nothing but a really nice tan.