Electrostatic attractions in proteins that bind with DNA

DNA structure above. Main attribute of DNA binding proteins is that they have some positively charged part that is attracted to negatively charged phosphate groups which hold DNA together. 

One very common part of proteins that bind to DNA is called zinc finger (zinc atoms shown as green spheres in above zinc finger examples). Zinc finger containing proteins can bind with DNA and stimulate or inhibit expression of gene that they influence. 

Arginine above is amino acid that has many amino groups which tend to have positive charges in body. Protamine is arginine rich protein that binds with DNA in sperm and keeps it more compact than DNA in other cell types. As side note very positively charged protamine can neutralize heparin (heparin looks like like polysaccharide that has many negative oxygen containing groups on sides) which causes coagulation as heparin has one of the largest density of negatively charged parts for molecule produced by body. This attribute of positively charged molecules in bloodstream may be dangerous if they bind with heparin.

Examples of arginine (shortened to R) proportions in different protamine sequences.

Due to small helical shape of protamine it can package DNA in sperm into ring shaped chromosome which is much smaller than histones that compact DNA in other cells.
 
Histones can bind or unbind from DNA depending on which charged modifications get added to histones.

If histones get acetylated by getting acetyl group shown above added to them then they seem to repel from DNA due to oxygen of acetyl group and oxygen of phosphate group on DNA repelling each other. Acetyl group gets usually added to positively charged lysine groups that would have been attracted to DNA.

DNA methylation involves methyl groups getting added to histones and usually it reduces gene expression as DNA wraps around these histones and is not open for RNA synthesis. Methyl groups have relatively positive charge compared to phosphate groups and this can add some binding capability. In some cases methylation can reduce binding with DNA if methyl groups get added to positively charged amino acids (arginine or lysine) in histones which probably have stronger attraction to DNA than methyl groups and in these cases genes are more likely to get expressed if only these positively charged parts get methylated.