  We present NIRCam and NIRISS modules for DOLPHOT, a widely-used crowded field
stellar photometry package. We describe details of the modules including pixel
masking, astrometric alignment, star finding, photometry, catalog creation, and
artificial star tests (ASTs). We tested these modules using NIRCam and NIRISS
images of M92 (a Milky Way globular cluster), Draco II (an ultra-faint dwarf
galaxy), and WLM (a star-forming dwarf galaxy). DOLPHOT's photometry is highly
precise and the color-magnitude diagrams are deeper and have better definition
than anticipated during original program design in 2017. The primary systematic
uncertainties in DOLPHOT's photometry arise from mismatches in the model and
observed point spread functions (PSFs) and aperture corrections, each
contributing $\lesssim0.01$ mag to the photometric error budget. Version 1.2 of
WebbPSF models, which include charge diffusion and interpixel capacitance
effects, significantly reduced PSF-related uncertainties. We also observed
minor ($\lesssim0.05$ mag) chip-to-chip variations in NIRCam's zero points,
which will be addressed by the JWST flux calibration program. Globular cluster
observations are crucial for photometric calibration. Temporal variations in
the photometry are generally $\lesssim0.01$ mag, although rare large
misalignment events can introduce errors up to 0.08 mag. We provide recommended
DOLPHOT parameters, guidelines for photometric reduction, and advice for
improved observing strategies. Our ERS DOLPHOT data products are available on
MAST, complemented by comprehensive online documentation and tutorials for
using DOLPHOT with JWST imaging data.
