HDAC inhibitor and how it works on a cellular level
Do you have a more specific question? The best I can give you is the mode of action that is generally seen across most biological mechanisms:

An HDAC inhibitor would cause inhibition by binding to HDAC, thus causing a conformational change that disallows the protein from being able to transfer  acetyl-groups to a histone-residue (cysteine I believe?).

Usually, if a protein is something that is abundant in cells, an inhibitors/activators work directly through bonding to the target to cause conformational changes. There is probably also another inhibitor that can bind directly to the HDAC-gene to cease its expression (but I don't see this being beneficial in a growing cell - but maybe in mature cells).