The basic scientific unit of plant classification is species. Each species falls under a genus, and each genus under an overarching family

The scientific name of species is written as Genus name (Capitalized, italic) + specific epithet (italic)

For example, the scientific name of Crimson Cattleya is Cattleya labiata.

Cattleya is the scientific name of the genus and labiata is the specific (species) epithet.

Most plants purchased from stores are horticultural cultivars. That is, they are new species that are intentionally created by plant breeders through careful selective cultivation. These are called varieties. 

The scientific name for a variety is written as Genus name (capitalized, italic) + specific epithet (italic) + 'cultivar name' (regular, single quotes, capitalized) 

Example: Vitis vinifera 'Kyoho'

Some varieties with complex hybrid backgrounds can omit the specific epithet and be written as genus name + 'cultivar name' (e.g. Rosa 'Graham Thomas'). 

Most hybrids come from the cross-breeding of different species within the same genus. Their scientific names can be written in two ways. The examples below are for the strawberry.

Option #1: genus name of female parent + specific epithet × specific epithet of male parent - e.g. Fragaria virgirniana × chiloensis

Option # 2 (if a new specific epithet is given to the hybrid) genus name (italic) × new specific epithet (italic), e.g. Fragaria × ananassa

If a hybrid is generated from two different genera, a new genus name is given, so "×" is placed before the new genus name. For example, the hybrid of Rhodohypoxis baurii and Hypoxis parvula is written as ×Rhodoxis hybrida.

Individuals within a single species may still vary considerably. Therefore, there are three taxonomic classes under species.

A morphologically distinct group of taxa of the same species sharing the same distribution area is called a variety. The distinguishing features are usually caused by environmental and geographic differences, and can be inherited stably.

The scientific name of the variety is written as Genus name (capitalized, italic) + specific epithet (italic) + var. (regular) + variety name (italic)

Example: Loropetalum chinense var. rubrum

(The use of subspecies as a classification is now discouraged for plants and used more for animals)

A subspecies is a group of individuals of the same species that are somewhat different from each other due to long periods of geographic or ecological isolation.

The scientific name of subspecies is written as Genus name (capitalized, italic) + specific epithet (italic) + subsp. (regular) + name of the subspecies (italic)

Example: Syringa reticulata subsp. amurensis

Forms come from minor differences within the original species due to environmental factors. Forms are usually unstable in terms of genetic inheritance.

The scientific name of a form is written as Genus name (capitalized, italic) + specific epithet (italic) + f. (regular) + form name (italic)

Example: Lamprocapnos spectabilis f. alba