Future exoplanet direct imaging instruments will be capability of detecting and spectrally characterizing Earth-like exoplanets, but which stars to observe, how long they should be observed, or how to follow up the detection of an exoplanet that appears Earth-like are still open questions.In this dissertation, I validate the probability based yield estimation technique, called completeness, for estimating single-visit blind search yield of the Nancy Grace Roman Space Telescope by simulating a Monte Carlo of full mission simulations. I show the Roman Coronagraphic Instrument (CGI) is largely sensitive to gas giants, planets that move relatively slowly in planet-star separation ($s$) and planet star difference in magnitude ($\Delta$mag) space over the instruments detection limits. Since future telescopes, like HabEx, have smaller inner working angles and a larger limiting $\Delta$mag, they are capable of detecting planets moving faster in ($s$,$\Delta$mag) space. Since the traditional completeness does not account for planetary motion, I created the exodetbox software package and Integration Time Adjusted Completeness to account for this planetary motion. I found that a design reference mission optimized with traditional completeness overestimates yield by 9.61% compared to Integration Time Adjusted Completeness. Once integration time adjusted completeness is calculated for a target star, dynamic completeness can be computed an order of magnitude faster than the traditional method. Post detection follow-up requires classification ways to compute temporal revisit parameters.I show how, even in our own solar system, an Earth-like planet can be confused with up to 6 other solar system planets. I present a method for computing the probability a planet is from a given sub-population. Since there are few methods to determine limiting or ideal times to follow-up the first detection, I also present methods to determine when to revisit as well as how long to revisit for. The exodetbox powered methods I introduce are computationally fast, provide a rich array of planet population data, and is a versatile backbone to planning revisits.