We present a detailed description of the first direct measurement of the spatial correlation function of X-ray selected AGN. This result is based on an X-ray flux-limited sample of 219 AGN discovered in the contiguous 80.7 deg^2 region of the ROSAT North Ecliptic Pole (NEP) Survey. Clustering is detected at the 4 sigma level at comoving scales in the interval r = 5-60 h^-1 Mpc. Fitting the data with a power law of slope gamma=1.8, we find a correlation length of r_0 = 7.4 (+1.8, -1.9) h^-1 Mpc (Omega_M=0.3, Omega_Lambda=0.7). The median redshift of the AGN contributing to the signal is z_xi=0.22. This clustering amplitude implies that X-ray selected AGN are spatially distributed in a manner similar to that of optically selected AGN. Furthermore, the ROSAT NEP determination establishes the local behavior of AGN clustering, a regime which is poorly sampled in general. Combined with high-redshift measures from optical studies, the ROSAT NEP results argue that the AGN correlation strength essentially does not evolve with redshift, at least out to z~2.2. In the local Universe, X-ray selected AGN appear to be unbiased relative to galaxies and the inferred X-ray bias parameter is near unity, b_X~1. Hence X-ray selected AGN closely trace the underlying mass distribution. The ROSAT NEP AGN catalog, presented here, features complete optical identifications and spectroscopic redshifts. The median redshift, X-ray flux, and X-ray luminosity are z=0.41, f_X=1.1*10^-13 cgs, and L_X=9.2*10^43 h_70^-2 cgs (0.5-2.0 keV), respectively. Unobscured, type 1 AGN are the dominant constituents (90%) of this soft X-ray selected sample of AGN.
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