On a standard QWERTY keyboard the "B" key is on the row above the spacebar, just below and right of the G and is normally typed using the index finger of the left hand. The character we know as uppercase B is assigned the decimal code 66 in Latin-1, ASCII, and Unicode character sets. In Windows, you can type an uppercase B with ALT+066 (on your numeric keypad) - a good trick to know if the B on your keyboard gets stuck. The code for lowercase b is 98 (ALT+098) in Latin-1, ASCII, and Unicode.

The Evolution of B
According to The American Heritage Dicionary of The English Language, third edition:

The second letter of the Phoenician alphabet stood for the sound of b in beth, "house." (glyph looked a bit like a 9) The Greeks altered its shape slightly and called it beta. (backwards 6) Eventually the upper loop was closed as beta evolved into the Roman capital B still used today.

The glyph (graphic representation) of both uppercase B and lowercase b can vary from one typeface to another depending on the whim and desires of the type designer. However, if a designer strays too far from the established familiar shapes their font becomes harder to read and less useful for communication.

The Shape of B
In today's typefaces, the glyph for uppercase B, even with its many variations and interpretations, is usually recognizable as two stacked loops on the right side of a vertical stem.

The classic roman B with serifs.		The clean, crisp look of sans serif.
Variations within the basic shape of B include extending the connection between the bowls beyond the vertical stem, making the loops solid, separating them completely or partially from the stem, and changing the shape or size of the bowls.

Lowercase b has one basic glyph, that is essentially the uppercase B without the upper loop.

The main distinctions in the lowercase b are the same characteristics shared by other similar glyphs in that face (such as d, h, or k) — tall or short descenders and large or small bowls.

Among script typefaces, capital B usually comes in one of these general variations:

This style of script B has a swash on top. It may be a simple extended serif or flourish or one with elaborate curls. The vertical stem may appear connected or as an all-in-one stroke, a loop, or a separate connected or unconnected stroke.
In this style of script B the swashes or curls are at the base of the bottom bowl or the vertical stem.