Because Superman is essentially invincible, the designers behind Superman Returns had to get a little clever with his vulnerability. Superman's biggest opponent is Metropolis itself, so you get a little green bar in the upper left-hand corner of the screen that keeps track of Metropolis' health (it's not in the target images here, so don't bother straining your eyes for it). The idea is that you have to defend the city and keep it healthy in order to succeed as Superman. It's not as if you have unlimited power either, a stamina meter just above Metropolis' health meter will show how super you can get before having to recharge by engaging in a little sunbathing.
Above: It's about scale, really. This is a fully-realized virtual city, ready to be stomped flat by a titanic adversary (Metallo piloting a giant mech).
Once Superman is charged up with solar power, he can use his super abilities, of which all the classics are represented: super breath, freeze breath and heat vision. These powers are selected with the control pad and then activated with the right trigger (the 360 version takes advantage of the analog trigger to focus the powers into a tighter beam when you pull the trigger harder). Tapping the control pad twice will engage the extreme version of a super power, which causes the standard gust of super breath to explode into a car-swirling, bystander-tossing tornado. Extreme heat vision was definitely the most exciting, though, instantly vaporizing a broad swath of Metropolis for about a 160-degree radius in front of Krypton's number one son... so, Superman's laser-apocalypse-vision didn't really look conducive to protecting Metropolis, but that level of devastation probably helps in the game's other zones, like Warworld.