We are undertaking a program to measure the characteristics of the intracluster light ( total flux , profile , color , and substructure ) in a sample of 10 galaxy clusters with a range of cluster mass , morphology , and redshift . We present here the methods and results for the first cluster in that sample , A3888 . We have identified an intracluster light ( ICL ) component in A3888 in V and r that contains 13 \pm 5 % of the total cluster light and extends to 700h _ { 70 } ^ { -1 } kpc ( \sim 0.3 r _ { 200 } ) from the center of the cluster . The ICL color in our smallest radial bin is V - r = 0.3 \pm 0.1 , similar to the central cluster ellipticals . The ICL is redder than the galaxies at 400 < r < 700 h _ { 70 } ^ { -1 } kpc although the uncertainty in any one radial bin is high . Based on a comparison of V - r color with simple stellar models , the ICL contains a component which formed more than 7 Gyr ago ( at z > 1 ) , coupled with a high metallicity ( 1.0 Z _ { \odot } < Z _ { ICL } \lesssim 2.5 Z _ { \odot } ) , and a more centralized component which contains stars formed within the past 5 Gyr ( at z \sim 1 ) . The profile of the ICL can be roughly fit by a shallow exponential in the outer regions and a steeper exponential in the central region . We also find a concentration of diffuse light around a small group of galaxies 1.4h _ { 70 } ^ { -1 } Mpc from the center of the cluster . In addition , we find 3 low surface brightness features near the cluster center which are blue ( V - r = 0.0 ) and contain a total flux of 0.1 M ^ { * } . Based on these observations and X-ray and galaxy morphology , we suggest that this cluster is entering a phase of significant merging of galaxy groups in the core , whereupon we expect the ICL fraction to grow significantly with the formation of a cD galaxy as well as the in-fall of groups .