The Spitzer Space Telescope Legacy Program SAGE-SMC allows global studies of resolved stellar populations in the SMC in a different environment than our Galaxy. Using the SAGE-SMC IRAC (3.6-8.0 mu m) and MIPS (24 and 70 mu m) catalogs and images combined with near-infrared (JHK sub(s)) and optical (UBVI) data, we identified a population of ~1000 intermediate- to high-mass young stellar objects (YSOs) in the SMC (three times more than previously known). Our method of identifying YSO candidates builds on the method developed for the Large Magellanic Cloud by Whitney et al. with improvements based on what we learned from our subsequent studies and techniques described in the literature. We perform (1) color-magnitude cuts based on five color-magnitude diagrams (CMDs), (2) visual inspection of multi-wavelength images, and (3) spectral energy distribution (SED) fitting with YSO models. For each YSO candidate, we use its photometry to calculate a measure of our confidence that the source is not a non-YSO contaminant, but rather a true YSO, based on the source's location in the color-magnitude space with respect to non-YSOs. We use this CMD score and the SED fitting results to define two classes of sources: high-reliability YSO candidates and possible YSO candidates. We found that, due to polycyclic aromatic hydrocarbon emission, about half of our sources have 3.6-4.5 and 4.5-5.8 colors not predicted by previous YSO models. The YSO candidates are spatially correlated with gas tracers.