  We present the Simple Intensity Map Producer for Line Emission (SIMPLE), a
public code for quickly simulating mock line-intensity maps, and an analytical
framework for modeling intensity maps including observational effects. SIMPLE
can be applied to any spectral line sourced by galaxies. The SIMPLE code is
based on lognormal mock catalogs of galaxies including positions and velocities
and assigns luminosities following the luminosity function. After applying a
selection function to distinguish between detected and undetected galaxies, the
code generates an intensity map, which can be modified with anisotropic
smoothing, noise, a mask, and sky subtraction, and calculates the power
spectrum multipoles. We show that the intensity autopower spectrum and the
galaxy-intensity cross-power spectrum agree well with the analytical estimates
in real space. We derive and show that the sky subtraction suppresses the
intensity autopower spectrum and the cross-power spectrum on scales larger than
the size of an individual observation. As an example application, we make
forecasts for the sensitivity of an intensity mapping experiment similar to the
Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) to the cross-power
spectrum of Ly$\alpha$-emitting galaxies and the Ly$\alpha$ intensity. We
predict that HETDEX will measure the galaxy-intensity cross-power spectrum with
a high signal-to-noise ratio on scales of $0.04\, h\,\mathrm{Mpc}^{-1} < k <
1\, h\,\mathrm{Mpc}^{-1}$.
