A methyl group can be added to a cytosine residue, usually one that neighbors a guanine (known as a CpG - cytosine-phosphate-guanine - site). This can affect chromatin and histone structures, as well as directly influencing binding of various factors, thereby altering the transcription of genes.
Cytosine residues in DNA that can be methylated (i.e. CpG sites) are likely to be in the same methylation state if they are geographically (proximally) close together. I can only find one paper that ...