What are the ways of classifying bread?

The Bread Baker's Apprentice has a 2-page long chart of different types of breads; in terms of classifying (not "describing") them, they look at the following:

• Water Content - literally the amount of water in the bread. From lowest to highest you have Stiff, Standard, or Rustic.

• Richness - the amount of fat, primarily, but also sugar, milk, eggs, or anything else to provide a richer mouth-feel.

• Fermentation - direct or indirect specifies whether or not there is pre-fermentation.

• Leavening - various categories describe the type of leavener used, including commercial yeast, wild yeast, chemical leavening, or a mix.

• Flatbreads have their own designation and can also describe unleavened breads.

That's enough to classify the vast majority of breads out there.

As far as "describing" bread goes, that is entirely subjective and culture-dependent. For anything more detailed, you really need to go and read a book - there's far too much literature to condense into a single Q&A thread.

This is a very general question, but I can see some use in it. If (for example) you have a recipe that says "shape into bâtards", that might not make any sense to the amateur.

So if you're looking for a straight definition of bread related terms; check out the baking glossary at the fresh loaf

As for the shapes of breads, this link from recipetips seems to be a good start.

Lifted from the first link:

Banneton: a woven basket, sometimes lined with linen, used to hold a shaped loaf while it is proofing.

Batard: a loaf that has an oval or oblong shape.

Biga: a term used variously as a very stiff (~50% hydration preferment), or as a generic term for preferment.

Boule: a round loaf (French for "ball").

Brotform: a coiled cane basket used to hold a shaped loaf while it is proofing.

Couche: heavy linen fabric used to hold formed loaves for proofing. The fabric can be pleated around the loaves to help them hold their shape.

Crumb: When a baker talks about the crumb they are talking about the pattern of holes inside of a loaf.

Fermentation: (1) the process by which yeast metabolizes sugars to produce carbon dioxide and alcohol (2) (aka bulk fermentation, first fermentation) the period of time the dough rests after mixing and before dividing/shaping.

Folding: one of the best ways of encouraging gluten development in slack doughs. Folding the dough consists of taking a wet dough out of the bowl, spreading it out a little on a clean, well-floured surface, folding it in thirds like a letter, rotating it 90 degrees and folding it up again, picking it up and dusting the loose flour off of it, and then returning the dough to the bowl and covering it again. Like punching down, folding degases the dough some, but it also encourages gluten development.

Gluten: "A tenacious elastic protein of wheat flour that gives cohesiveness to dough." Gluten is what allows bread dough to develop those long, beautiful strands and create large open pockets of air (think about the inside of a loaf of Ciabatta compared to the inside of a muffin). Bread flours tend to be made from hard wheats that are higher in protein than regular flour, providing more gluten.

Hydration: the ratio of liquid ingredients (primarily water) to flour in the dough. A dough with 500g of flour and 340g of water has a hydration of 68% (340/500).

Lame: a thin blade on a handle, used to score (slash) loaves before baking.

Levain: usually used as a synonym for sourdough.

Pâte fermentée (aka prefermented dough): a type of preferment in which the ingredients (flour, water, yeast, salt) are mixed in the same proportion as (usually) a basic white bread dough at about 65% hydration.

Poolish: A type of sponge. Typically quite wet, an equal weight of water and flour with an extremely small amount of yeast. For my batch of two French Bread loaves, I typically use 8 ounces of water, 8 ounces of bread flour, and 1/8 teaspoon a instant yeast. Mix it, cover the bowl, and leave it at room temperature overnight.

Proof: (1) the final rise of the shaped loaves before baking (2) the hydration of dry active yeast in water before it is added to the dough

Score (aka slash or dock): to cut the surface of the loaf prior to baking. This provides for controlled expansion of the loaves during baking so they do not “break” undesirably. Scoring is also used to enhance the appearance of the bread.

Sourdough: a preferment that is a culture of wild yeast and bacteria that is perpetuated by the periodic addition of flour and water, or a bread leavened in whole or part by this culture.

sponge: Also known as a "preferment," a sponge is a portion of the ingredients that is mixed ahead of time, typically overnight. Using a sponge extends the fermentation process longer and generally releases more complex flavors in your loaf. It can also be used to soften dry ingredients (such as whole grains) and release sugars from the grains.

As for judging crumb, my favorite two terms used by German Meister Bakers are juicy (saftig) and woolly (wollig).

The first, praise for tarter breads such as sour rye; the second for toast bread and lunch rolls.

An unflattering term would be cotton (Baumwolle) for flavorless and dry fluff.