Some taxonomy basics:

One of many pneumonics to remember this particular organizational structure is: Daring Kangaroos Play Cellos, Orangutans Fiddle, The Gorillas Sings Special Songs. (Variants on the primary seven groups include: "Karen, please come over for great sex;" "King Philip came over for great sex;" etc.)

The Plant Kingdom or Plantae is a group whose members are today defined by the presence of green chloroplasts containing chlorophyll and carotinoid pigments and are able to create energy using light and minerals.

Plant Divisions or Phyla:

Phylum names traditionally end in phyta. As with kingdoms, these divisions or phyla are evolving and the members shifting as our knowledge and genetic techniques improve. The initial four divisions: Thallophyta (bacteria, algae, fungi), Bryophyta (mosses and liverworts, Pteridophyta (ferns and cubmosses) and Spermatophyta (seed plants: gymnosperms and angiosperms) have been split and expanded and there is debate about these divisions. The groupings are largely based on reproductive characteristics and tissue structure. This table below is from the Wiki on Phylum (see Wiki Ansers on Plant phylum or UCMP Berkeley for a different scheme: http://www.ucmp.berkeley.edu/help/index/plantae.html)

In the largest complex phylum, Anthrophyta previously called Magnoliophyta (flowering plants), classification becomes even more contentious. The flowering plants have historically been divided into two Classes based on the number of cotyledons on the embryo. Those flowering plants with two cotyledons are called dicots while those with only one are called monocots (see UCMP Berkeley  Discussion of Classes). Systematists argue for more classes, different classes and more levels. For simplicity sake, there are two classes:

• Dicotyledoneae

• Monocotyledoneae

Within classes, are Orders which organize finer detail. It is a subjective art choosing which characteristics to consider forming into a groups. While there is much debate on this organization, here is one useful classification structure.

"The APG II system does not assign the monocots to a taxonomic rank, instead recognizing a monocots clade. This system recognizes ten orders of monocots and two families of monocots not yet assigned to any order" (Wiki Monocots see discussion of Cladistics)

Family

Once again, both vegetative and reproductive features are used to characterize families, e.g. kind and number of pistils, stamens, carpal, fruit type, flower and leaf form, etc. With few exceptions, family names end in -ceae. Families often share similar cultural requirements and are prone to similar diseases and pests. For instance, insects coevolved with plants. As the flowering plants, Anthophyta, underwent divergence so to did herbivores and pollinators. Thus if we want to attract beneficial predatory insects to the garden we should select plants with short flower tubes, e.g. carrot family (Apiaceae  syn. Umbelliferae), mustard family (Brassicaceae), mint family (Lamiaceae) and aster family (Asteraceae). Disease susceptibility can also be predicted across families although there will be some members with greater resistance and often disease and pest pressures select for and shape the development of the various genera.

Genus

The differences between members of a genus become more subtle. They will share similarities in physical characteristics that belie their common genetics. However, it is sometimes discovered that the physical characteristics are coincidental, in which case members will be shifted and to other groupings. For instance, the goldenrods were once lumped together within the genus Solidago. It was recently found that the Grass-leaved Goldenrods were not that closely related and have been moved to the genus Euthamia (see for instance John Semple Goldenrods).

 Similarity of flowers and fruits is the most widely used feature, although roots, stems, buds, and leaves are also used. Common names typically apply to genera. For example Hemerocallis is the genus of daylilies, Acer is the genus of maples, and Viburnum the genus of viburnum. (Note when a genus name is used as a common name, it is not capitalized).

Species

Species are a group of plants that conform to certain fixed properties. Naturally occurring populations interbreed at maturity and sustain these properties. While there may be clusters of variations or phenotypes, they are sufficiently similar to be grouped together. Modern genetic techniques have been helpful to define particular genotypes associated with specific species. (See Wiki on Species and Species Problem).
 

Species naming conventions

Common names are lower case unless the word is derived from a surname or proper noun, e.g. tomato, Kentucky coffee tree, black-eyed Susan, Douglas fir, etc. Botanical names are often used as common names in which case they are set in lower case and not italicized, e.g. rhododendron, hosta, iris, etc.

Botanical names for a given species are given as genus name or abbreviation followed by species name and variety name as follows.

• Genus names are italicized and the first letter capitalized, e.g. Solanum

• Species name follows the genus name and is italicized an given in lower case Solanum lycopersicum or S. lycopersicum

• Sometimes, the plant name is followed by the abbreviated name of the individual who first named the plant - the "authority."  This can be designated by a letter or the name, e.g.

Quercus alba L. here the the letter "L" is used to identify Linnaeus as the authority or Acer saccharum Marsh where Humphrey Marshal is recognized as the name's author. 

• Sub-species, varieties, and form (f) names must consist of only lower-case letters and must be printed in italics (or underscored). The sub-division names, or their abbreviations, must never be italicized – eg. Gleditsia triacanthos var. inermis, Drosera binata ssp. multifida f. extrema.

• The cultivar name is capitalized and enclosed in single quotes e.g. Solanum lycopersicum 'Big Boy' or S. lycopersicum 'Big Boy' or if there is no ambiguity, S. Big Boy'

Hybrids

(The following is excerted from Glenn L. Roberts University of Guelph Lecture on Taxonomy)

A hybrid is the offspring of two plants from different taxa (different species, genera, family, etc.). For example, an intergeneric hybrid is a hybrid between species of two different genera. An interspecific hybrid is a hybrid between two different species of the same genus.

Take the example of a cross between the two species Salix aurita L and Salix caprea L. The hybrid name would be:

Salix aurita L X S. caprea L. (this is naming according to a formulae)

Naming according to a formal name would be the example of the cross between Quercus alba L. and Quercus michauxii Nutt.

Quercus X beadlei Trel. (this is naming according to a formal name)

As you can see, naming of hybrids is a bit more complicated, but both forms shown above are acceptable according to the ICBN and you will see both used in books and catalogues. The important thing to note is that in either naming convention an “X” is used to depict the hybrid designation. This is the thing to watch out for. If you see the “X”, you know that it is a hybrid between two plants. However, the name does not always tell what the two plants are (as in the Quercus example).

(The following is excerted from Bob & Lynn Wellenstein Names and Naming.) 

There are two different but related sets of rules for plant nomenclature. Plants growing in their native habitat are named under The International Code of Botanical Nomenclature (ICBN), and plants cultivated and hybridized by humans are named under the rules of The International Code of Nomenclature for Cultivated Plants.

...take [the slipper orchid]  Paph. glaucophyllum var. moquettianum 'Candor Rose Gold' AM/AOS and cross it with Paph. adductum 'Candor Wildwood' HCC/AOS. The cross, if unregistered, would be listed capsule parent first and pollen parent second separated by an "x" as (Paph. glaucophyllum var. moquettianum 'Candor Rose Gold' AM/AOS x Paph. adductum 'Candor Wildwood' HCC/AOS). As it happens this cross has already been made and flowered, and was named as Paph. Bianka by H. Doll in 1990. It should be noted at this point that if the reciprocal cross were made, that is (Paph. adductum x Paph. glaucophyllum) it will still be considered the same cross and named Paph. Bianka. The same applies if the cross is made with different parental clones, any cross of either Paph. glaucophyllum or Paph. moquettianum with Paph. adductum, regardless of clones used, or which was capsule and which was the pollen parent, will be Paph. Bianka. Also note that if a plant of Paph. Bianka is selfed or crossed with another plant of Paph. Bianka, the resultant progeny will also be considered Paph. Bianka. The flower pictured is Paph. Bianka 'Candor Autumn Tapestry' AM/AOS. As you can see, there are a few different rules for writing hybrid names. First, they are not italicized or underlined, and secondly, all words are capitalized."