One of my favorite articles about antioxidant mechanisms:
Prior, R. L., Wu, X. L., & Schaich, K. (2005). Standardized methods for the determination of antioxidant capacity and phenolics in foods and dietary supplements. Journal of Agricultural and Food Chemistry, 53, 4290-4302.
Try the Ferrous Ion Chelating Assay which is an excellent assay and relatively easy to do. Also try the beta carotene bleaching assay. Check my thesis on how to perform these assays.