This means that classifications at the domain, phylum, class, order, and suborder begin with a capital letter but are not italicized. Levels from family to species are in italics and capitalized, except species, which is not capitalized. For example, Mycobacterium tuberculosis is in the family Mycobacteriaceae, order Actinomycetales. If a generic plural for an organism exists, it is neither capitalized nor italicized.
For clarity, I sometimes like to add the level of classification as an adjective, e.g., "an isolate from the class Actinobacteria". This is a courtesy, and as far as I know not part of the International code. Also Bergey's writes Alphaproteobacteria (all one word), so we use that convention.
In addition, while I strive to avoid Gram stain classification unless we have actually done a Gram stain, this is sometimes unavoidable. "Gram" refers to the test's inventor, Hans Christian Gram. Because this is a test of physiology and not phylogeny, this is not included in the International nomenclature code. According to the CDC guidelines on the Gram test, the name of the stain is capitalized (Gram-stain) but the result is not (gram-, gram+).