Genes can be deemed “on” or “off” depending on whether they are expressed or not. In some cases expressed genes exhibit a specific phenotype or function thus if the phenotype or the function is not observed then the gene is probably not expressed and is therefore “off.”
Chromatin control access to genes within cells. Histones on chromosomes contain chemical tags that act as switches to control access to DNA and turn genes on and off. A direct measure of gene activity is to monitor the production of mRNA by that gene as with microarray chips.
Microarrays are also used to deem whether a potential gene is on or off. A microarray is a collection of DNA spots that measure expression levels of genes. Due to the nature of microarrays, large numbers of genes may be tested at once. The DNA spots are microscopic and contain a specific gene code that is hybridized with cDNA or cRNA or mRNA. The more matches, the more tightly the DNA becomes hybridized. When the non relevant interactions are washed away we are left with hybdridized DNA that can suggest what genes are on or off. Gene expression is shown through hybridization of mRNA with DNA. 
- U.S. Department of Health and Human Services. The New Genetics. October 2006.<http://www.nigms.nih.gov>.