Broadly speaking, Port from Portugal has two general styles, Ruby and Tawny. Within these two general categories are several subcategories.

Ruby

True Vintage Port is the star; typically produced only in exceptional vintages, this wine spends two years in cask before being bottled, where it will slowly age to perfection over the next 15 to 20 years. Not intended to drink young, this style is tannic and brash with aggressive ripe blackberry fruit, tar, and molasses. As it ages, it becomes smoother and mellower with a wealth of secondary flavors including dried fruit, cocoa, cigar box, and cinnamon spice. These are relatively rare and expensive.

Because Vintage Port takes many years to age, a similarly styled, less expensive version was designed. Late Bottled Vintage spends four to six years in cask, which allows it to age more quickly before being bottled. With similar flavors to Vintage Port but in a softer more accessible style, this is ready to drink upon release.

Bottles labeled Ruby or Reserve are typically the least expensive and most straightforward. Most are multivintage blends and offer grapey sweet aromas with blackberry jam flavors and earthy spice notes.

Tawny

Tawny Port is quite different. Aged for many years in old wooden casks before blending, these slowly oxidize and lose their color, mellowing into a light brown liquid with none of the aggressive grapey berry jam notes of the Ruby style; instead, they offer notes of smoky dried fruits, wood, caramel, butterscotch, and toffee. 

Higher-quality examples will state on its label average age (for example, Ten Year Tawny, Twenty Year Tawny). If no age is given, this typically is a blend of red and white wines (to achieve the correct color) that is aged less than seven years. 

Colheita refers to a Tawny style from one particular vintage. Not to be confused with Vintage Port, these will taste like a Tawny Port.

White Port is typically relatively dry and served as an aperitif, often mixed with tonic water.

New World examples mimic either the Ruby or Tawny style and state so on the label. Australia has had success with Tawny Port styles; South Africa and California also produce some fine examples.