While color vision is tested at Military Entrance Processing Stations (MEPS), normal color vision is not a requirement to join the U.S. Military.
However, many military jobs require normal color vision. This is because there is some operational or safety aspect of the job that requires one to be able to distinguish between colors (indicator lights, smoke flares, etc.). Because of this, color vision requirements are not waiverable for military jobs which require normal color vision.
The military defines "normal color vision" by use of one of three tests: the Pseudoisochromatic Plate (PIP) Set, Farnsworth Lantern (FALANT), or the OPTEC 900 Color Vision Tester. You don't get to choose which test to use. It depends on what is in use at the particular MEPS where you have your physical.
The Pseudoisochromatic Plates are painted pictures showing an assemblage of color dots with a number in the middle made with different colored dots. To pass this test, you can have no more than four errors in the 14 plate set.
The Farnsworth Lantern involves colored signal lights that have to be identified from a distance. Two lights are shown at once, and the person being tested must identify the color (red, green, or white). The lights, however, are darkened with a filter to prevent people who are colorblind from being able to tell colors apart by their brightness. To pass this test you can have no errors.
The OPTEC 900 Color Vision Tester a modern version of the Farnsworth Lantern Test. Subjects are presented with pairs of red, white, and green lights and are required to name the colors. Like the Farnsworth Lantern, you must name the colors with no errors in order to pass this test.
Some military jobs (mostly in the Army and Marine Corps) only require red/green color discrimination. This means you could still qualify for that job if you fail the color vision test, but show the ability to be able to distinguish between vivid green and vivid red.