Some people recommend vacuuming your mattress and then cleaning it with baking soda. While it is important to clean your mattress regularly, and ideally flip it twice a year, this does not really qualify as deep cleaning.
Deep cleaning a mattress is something that can’t really be done by yourself. It requires specialist equipment and cleaning products that only mattress cleaning professionals have. This is the only way to be sure your mattress is completely free of germs, dirt and dust mites.