Searches for slow radio transients and variables have generally focused on extragalactic populations, and the basic parameters of Galactic populations remain poorly characterized. We present a large 3 GHz survey performed with the Allen Telescope Array (ATA) that aims to improve this situation: ASGARD, the ATA Survey of Galactic Radio Dynamism. ASGARD observations spanned 2 years with weekly visits to 23 deg^2 in two fields in the Galactic Plane, totaling 900 hr of integration time on science fields and making it significantly larger than previous efforts. The typical blind unresolved source detection limit was 10 mJy. We describe the observations and data analysis techniques in detail, demonstrating our ability to create accurate wide-field images while effectively modeling and subtracting large-scale radio emission, allowing standard transient-and-variability analysis techniques to be used. We present early results from the analysis of two pointings: one centered on the microquasar Cygnus X-3 and one overlapping the Kepler field of view (l = 76{deg}, b = +13.5{deg}). Our results include images, catalog statistics, completeness functions, variability measurements, and a transient search. Out of 134 sources detected in these pointings, the only compellingly variable one is Cygnus X-3, and no transients are detected. We estimate number counts for potential Galactic radio transients and compare our current limits to previous work and our projection for the fully-analyzed ASGARD dataset.
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