Local primordial non-Gaussianity (PNG) is a promising observable of the
underlying physics of inflation, characterized by a parameter denoted by
${f}_{\mathrm{N}\mathrm{L}}$ . We present the methodology to measure local ${f}_{\mathrm{N}\mathrm{L}}$ from the
Dark Energy Survey (DES) data using the 2-point angular correlation function
(ACF) via the induced scale-dependent bias. One of the main focuses of the work
is the treatment of the integral constraint. This condition appears when
estimating the mean number density of galaxies from the data and is especially
relevant for PNG analyses, where it is found to be key in obtaining unbiased
${f}_{\mathrm{N}\mathrm{L}}$ constraints. The methods are analysed for two types of
simulations: $\sim 246$ GOLIAT N-body simulations with non-Gaussian initial
conditions ${f}_{\mathrm{N}\mathrm{L}}$ equal to -100 and 100, and 1952 Gaussian ICE-COLA mocks
with ${f}_{\mathrm{N}\mathrm{L}}=0$ that follow the DES angular and redshift distribution. We
use the GOLIAT mocks to asses the impact of the integral constraint when
measuring ${f}_{\mathrm{N}\mathrm{L}}$ . We obtain biased PNG constraints when ignoring the
integral constraint, ${f}_{\mathrm{N}\mathrm{L}}=-2.8\pm 1.0$ for ${f}_{\mathrm{N}\mathrm{L}}=100$
simulations, and ${f}_{\mathrm{N}\mathrm{L}}=-10.3\pm 1.5$ for ${f}_{\mathrm{N}\mathrm{L}}=-100$ simulations,
whereas we recover the fiducial values within $1\sigma $ when correcting for the
integral constraint with ${f}_{\mathrm{N}\mathrm{L}}=97.4\pm 3.5$ and ${f}_{\mathrm{N}\mathrm{L}}=-95.2\pm 5.4$ ,
respectively. We use the ICE-COLA mocks to validate our analysis in a DES-like
setup, finding it to be robust to different analysis choices: best-fit
estimator, the effect of integral constraint, the effect of BAO damping, the
choice of covariance, and scale configuration. We forecast a measurement of
${f}_{\mathrm{N}\mathrm{L}}$ within $\sigma ({f}_{\mathrm{N}\mathrm{L}})=31$ when using the DES-Y3 BAO sample,
with the ACF in the $1\text{}\mathrm{d}\mathrm{e}\mathrm{g}\theta 20\text{}\mathrm{d}\mathrm{e}\mathrm{g}$ range.