We use new WFC3 observations of the nearby grand-design spiral galaxy M83 to develop two independent methods for estimating the ages of young star clusters. The first method uses the physical extent and morphology of H alpha emission to estimate the ages of clusters younger than tau approximate to 10 Myr. It is based on the simple premise that the gas in very young (tau < a few Myr) clusters is largely coincident with the cluster stars, is in a small, ring-like structure surrounding the stars in slightly older clusters since massive star winds and supernovae have had time to push out the natal gas (e.g., tau approximate to 5 Myr), and is in a larger ring-like bubble for still older clusters (i.e., approximate to 5-10 Myr). If no H alpha is associated with a cluster it is generally older than approximate to 10 Myr. The second method is based on an observed relation between pixel-to-pixel flux variations within clusters and their ages. This method relies on the fact that the brightest individual stars in a cluster are most prominent at ages around 10 Myr, and fall below the detection limit (i.e., M-V < -3.5) for ages older than about 100 Myr. Older clusters therefore have a smoother appearance and smaller pixel-to-pixel variations. The youngest clusters also have lower flux variations, hence the relationship is double valued. This degeneracy in age can be broken using other age indicators such as H alpha morphology. These two methods are the basis for a new morphological classification system which can be used to estimate the ages of star clusters based on their appearance. We compare previous age estimates of clusters in M83 determined from fitting UBVIH alpha measurements using predictions from stellar evolutionary models with our new morphological categories and find good agreement, at the approximate to 95% level. The scatter within categories is approximate to 0.1 dex in log tau for young clusters (< 10 Myr) and approximate to 0.5 dex for older (> 10 Myr) clusters. A by-product of this study is the identification of 22 "single-star" H II regions in M83, with central stars having ages approximate to 4 Myr.