An acid is a compound that donates hydrogen ions when dissolved in water. When it does this, it also releases the ions to which the hydrogens were bound before the compound was put in solution. A hydrogen ion is positively charged and is known as a cation while the ion to which it was attached is negatively charged and is known as an anion. The anion is the prime consideration when naming the acid. The rules are simple, but they are different depending on whether the acid is binary, which means it comes from a compound containing hydrogen and one other element, or oxo, which means the hydrogen is attached to a polyatomic ion that contains oxygen.
Binary acids begin with "hydro-" and end in "-ic." Oxo acids don't use the "hydro-" prefix. If the name of the anion ends in "-ate," the name of the acid ends in "-ic," and if the name of the anion ends in "-ite," the name of the acid ends in "-ous."
A binary acid contains only hydrogen and another element. To distinguish this from an oxo acid, the name always starts with "hydro-" in reference to the hydrogen atom. The second term in the name is that of the anion, and it's easy to name this. You simply change the last few letters in the element's name to "-ic." Finally, add the word "acid," and you're done.
For example, the compound HCl is composed of hydrogen and chlorine, and in solution it produces a strong acid. To name this acid, start with "hydro-," then change the name of the anion from chlorine to chloric. Tack on the word "acid" and you have hydrochloric acid. Here are two other examples:
Hydrogen commonly forms compounds with polyatomic ions that contain oxygen. When such a compound dissolves in water to form an acid, the polyatomic ion is the anion. The first thing to remember is that, because these are not binary acids, you don't use the prefix "hydro" when naming them. The name of the acid comes solely from the nature of the anion.