MaNGA (Mapping Nearby Galaxies at Apache Point Observatory) is an integral-field spectroscopic survey of 10,000 nearby galaxies that is one of three core programs in the fourth-generation Sloan Digital Sky Survey (SDSS-IV). MaNGA's 17 pluggable optical fiber-bundle integral field units (IFUs) are deployed across a 3 deg field, they yield spectral coverage 3600-10,300 Ang at a typical resolution R ~ 2000, and sample the sky with 2" diameter fiber apertures with a total bundle fill factor of 56%. Observing over such a large field and range of wavelengths is particularly challenging for obtaining uniform and integral spatial coverage and resolution at all wavelengths and across each entire fiber array. Data quality is affected by the IFU construction technique, chromatic and field differential refraction, the adopted dithering strategy, and many other effects. We use numerical simulations to constrain the hardware design and observing strategy for the survey with the aim of ensuring consistent data quality that meets the survey science requirements while permitting maximum observational flexibility. We find that MaNGA science goals are best achieved with IFUs composed of a regular hexagonal grid of optical fibers with rms displacement of 5 microns or less from their nominal packing position, this goal is met by the MaNGA hardware, which achieves 3 microns rms fiber placement. We further show that MaNGA observations are best obtained in sets of three 15-minute exposures dithered along the vertices of a 1.44 arcsec equilateral triangle, these sets form the minimum observational unit, and are repeated as needed to achieve a combined signal-to-noise ratio of 5 per Angstrom per fiber in the r-band continuum at a surface brightness of 23 AB/arcsec^2. (abbrev.) ; Comment: 18 pages, 16 figures. Accepted for publication in AJ. Version with full resolution figures is available at http://www.stsci.edu/~dlaw/Papers/MaNGA_Observing.pdf