Observations of the Sun at millimeter and submillimeter wavelengths offer a unique probe into the structure, dynamics, and heating of the chromosphere; the structure of sunspots; the formation and eruption of prominences and filaments; and energetic phenomena such as jets and flares. High-resolution observations of the Sun at millimeter and submillimeter wavelengths are challenging due to the intense, extended, low-contrast, and dynamic nature of emission from the quiet Sun, and the extremely intense and variable nature of emissions associated with energetic phenomena. The Atacama Large Millimeter/submillimeter Array (ALMA) was designed with solar observations in mind. The requirements for solar observations are significantly different from observations of sidereal sources and special measures are necessary to successfully carry out this type of observations. We describe the commissioning efforts that enable the use of two frequency bands, the 3-mm band (Band 3) and the 1.25-mm band (Band 6), for continuum interferometric-imaging observations of the Sun with ALMA. Examples of high-resolution synthesized images obtained using the newly commissioned modes during the solar-commissioning campaign held in December 2015 are presented. Although only 30 of the eventual 66 ALMA antennas were used for the campaign, the solar images synthesized from the ALMA commissioning data reveal new features of the solar atmosphere that demonstrate the potential power of ALMA solar observations. The ongoing expansion of ALMA and solar- commissioning efforts will continue to enable new and unique solar observing capabilities.