We report continuous surface observations of carbon dioxide (CO2) and methane (CH4) from the Los Angeles (LA) Megacity Carbon Project during 2015. We devised a calibration strategy, methods for selection of background air masses, calculation of urban enhancements, and a detailed algorithm for estimating uncertainties in urban-scale CO2 and CH4 measurements. These methods are essential for understanding carbon fluxes from the LA megacity and other complex urban environments globally. We estimate background mole fractions entering LA using observations from four "extra-urban" sites including two "marine" sites located south of LA in La Jolla (LJO) and offshore on San Clemente Island (SCI), one "continental" site located in Victorville (VIC), in the high desert northeast of LA, and one "continental/mid-troposphere" site located on Mount Wilson (MWO) in the San Gabriel Mountains. We find that a local marine background can be established to within ~1 ppm CO2 and ~10 ppb CH4 using these local measurement sites. Overall, atmospheric carbon dioxide and methane levels are highly variable across Los Angeles. "Urban" and "suburban" sites show moderate to large CO2 and CH4 enhancements relative to a marine background estimate. The USC (University of Southern California) site near downtown LA exhibits median hourly enhancements of ~20 ppm CO2 and ~150 ppb CH4 during 2015 as well as ~15 ppm CO2 and ~80 ppb CH4 during mid-afternoon hours (12:00-16:00 LT, local time), which is the typical period of focus for flux inversions. The estimated measurement uncertainty is typically better than 0.1 ppm CO2 and 1 ppb CH4 based on the repeated standard gas measurements from the LA sites during the last 2 years, similar to Andrews et al. (2014). The largest component of the measurement uncertainty is due to the single-point calibration method; however, the uncertainty in the background mole fraction is much larger than the measurement uncertainty. The background uncertainty for the marine background estimate is ~10 and ~15 % of the median mid-afternoon enhancement near downtown LA for CO2 and CH4, respectively. Overall, analytical and background uncertainties are small relative to the local CO2 and CH4 enhancements; however, our results suggest that reducing the uncertainty to less than 5 % of the median mid-afternoon enhancement will require detailed assessment of the impact of meteorology on background conditions.