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Depending on how your skin is feeling, you may prefer either a manual or chemical exfoliant to remove dead skin cells. A manual exfoliant is a physical scrub.  This can a warm washcloth, baking soda, or any of various products specifically designed for the purpose of exfoliation, like facial brushes. Anything that can manually scrub your skin.  While manual exfoliation is more natural, be careful about further irritating the skin, as it can be abrasive. Chemical exfoliants come in several forms. Two common and effective ones are BHAs and Retinoids.  A BHA exfoliant uses Beta Hydroxy Acid, which contains salicylic acid, to get deep inside your pores, dissolve dirt, and exfoliate the skin. Acne marks will fade faster and you should get fewer breakouts.   Retinoid creams can be used to speed up the skin's natural process of cell division, which pushes out the discolored skill cells. This treatment will increase sensitivity to sunlight, so be sure to apply the cream at night. Making sure to choose a gentle exfoliant (so as not to further irritate the skin), scrub with either a manual or chemical exfoliant every morning and apply a retinoid cream every night.
Try manual exfoliation first. Try chemical exfoliants if manual ones don't work. Use exfoliants every morning and evening.