The minimalist style typically consists of fine line compositions with little to no shading or coloring, affecting a look reminiscent of the illustrations in an old 1800s text book. Whatever shading is present, is usually accomplished by non-traditional tattoo means, such as stippling (small dots that add depth and shading depending upon how closely and numerously they are clustered together), or by hatching / cross-hatching (using lines to create depth and shading, depending upon their spacing).
Do not be fooled by the name of this style, though. Despite its simplified appearance, this style is incredibly difficult to reproduce. With such thin line work and no shading or coloring to butt it up against, there is absolutely no room for error.