Here we present the results of an exploration of the Laguerre-Gaussian (LG) modes of laser light. These modes, each characterized by an integral index l, carry orbital angular momentum due to their helical phase fronts. We demonstrate methods of generating the LG modes from a simple Gaussian mode using computer-generated holograms and find that we can generate each of the LG modes with indices l = -3 through l = 3. We also predict and confirm the behavior of positive and negative LG modes in a superposition. The intensity pattern of a superposition of an LG mode with index l and one with index -l is a symmetric arrangement of 2l bright spots which rotate as the relative phase between the two beams is adjusted. Finally, we explore an interferometric method of sorting even and odd modes from a superposition and nd that we can separate an l = 0 mode and an l = 1 mode from a superposition of the two.