Right can be a noun (you have a right), a verb (right this wrong), an adjective (my right foot), or an adverb (right after bedtime). Rightly is an adverb only (rightly dressed). Both right and rightly can be used as adverbs to modify verbs (Spell it right or rightly), but only rightly is standard in the meaning of "properly": "The arrested man rightly refused to talk to the police." Both right and the plural rights have many additional meanings, but one can avoid overusing such already-hackneyed expressions as "be in one's right mind," "put things right," "the right thing at the right time," "right of way," "right wing," "right about-face," "right away," "out in right field," "let the left hand know what the right hand is doing," "right to work," "in one's own right," "in the right," "by rights," and "set to rights." "Right along," "right soon," "right off," and "right smart" are informal and not-recommended phrases indicating the use of right as an adverb.
Dictionary of problem words and expressions. Harry Shaw. 1975.