How does an SDS PAGE gel work?

An SDS-PAGE gel contains the ionic detergent SDS (sodium dodecyl sulfate). SDS disrupts the tertiary structure of proteins, bringing the folded proteins down to linear molecules. It also coats the proteins in a uniform negative charge. The SDS present in the gel also makes sure that the linearized proteins stay that way throughout the run. 

When a current is applied to the gel, all SDS-bound, negatively-charged proteins in a sample start migrating through the gel toward the positive end of the gel. The sieving effect of the gel matrix allows smaller-sized protein molecules to travel through the gel faster because of their smaller mass. The proteins are thus separated according to their size. There is no differential migration based on charge as all SDS-coated proteins have the same charge-to-mass ratio.