So, I have been watching a lot of videos on physics, and a few of them have eluded to the fact that light has momentum. For instance, minutephysics video "E=MC^{2}" is incomplete states that the full equation to describe objects with momentum and mass is E^2= (mc^2)^2 + (pc)^2 and he also says "The energy of a massless particle is the same as it's momentum". What I don't understand is this: The equation for an objects momentum is P=(mv)/(sqrt(1-(v^2/c^2))) which is basically just p=mv but because of gamma you have to do that annoying thing in the denominator. But EITHER WAY when mass=0, momentum equals zero. And light is massless. So... I'm confused. Please help.

Volumes have been written about this. The modern concept of light was started by Plank and Einstein. The photoelectric effect gave experimentally that the energy of a photon is a function of it's frequency only. The zero mass was an hypothesis initially but has been verified experimentally to a high precision. Quantum mechanics is full of non-intuitive results when viewed from the perspective of classical mechanics. Relativity is an extension of classical mechanics when velocities are near the speed of light.

If you want to get a really good introduction get a copy of Richard Feynman's book "QED" Quantum Electro Dynamics.