There are several epigenetic ways that a gene can be modified, that is having its expression altered without changes to its DNA. Two of the most widely studied are DNA methylation and histone modification.
1) DNA methylation - where methyl groups latch onto parts of a DNA sequence and can switch a gene on or off.
2) Histone modification - DNA winds around histone proteins for compaction and gene regulation, but certain epigenetic factors can bind to the histones which affects the extent to which DNA winds around the protein. This effects gene expression.