This article does not orient you to older board configurations or to other components on the board, nor does it go into any detail about specific properties of the pins themselves. That information is readily available elsewhere, but a good start is this article with more information about Arduino pins and their properties.
Most Arduino boards are the same shape and size for standardization and interchangeability: a small rectangle about 2.25X2.75 Inches with USB and power ports on one of the short edges, and two rows of header sockets along the two long edges. The headers are narrow, tall blocks, each with a single row of small holes (sockets) along the center of the top face. Each Arduino pin is associated with one of these sockets.
Holding the board with the end that includes the USB and power ports at the top, the headers run vertically along the left and right edges. Both left and right headers are divided into lower and upper sections separated by a small notch. Unfortunately, some headers are manufactured without this notch, making tactile orientation a little harder.Check out this post on dealing with notchless headers for suggestions. In the modern R3 header configuration, the left header has 6 sockets in the lower section and 8 in the upper. The right header has 8 sockets in the lower section and 10 in the upper.
Note: Older boards have header configurations with fewer sockets in the top sections on both left and right.
The lower-left section of 6 sockets is the Analog Section. In order from bottom to top, the sockets are:
A5, A4, A3, A2, A1, and A0.
The top-left section of 8 sockets is mostly related to power supply. From bottom to top, these sockets are:
voltage in, ground pin, another ground pin, 5 volt pin, 3 volt pin, reset pin, I/O reference pin, and an unused pin.
The lower-right header section of 8 sockets is where the digital pins begin. From bottom to top, these are:
D0, D1, D2, D3, D4, D5, D6, and D7.
The top-right header section of 10 sockets continues the digital pins. From bottom to top, the sockets are:
D8, D9, D10, D11, D12, D13, ground pin, analog ref pin, I2C SDA, and I2C SCL.
Non-Visual Techniques for Navigating The Sea of Holes
It’s not easy to feel the sockets in the headers with your fingertips, but there are other ways. Counting the sockets is easy using a probe such as a tooth pick, stiff piece of wire, or an opened paper clip, but you get serious old-school blind cred if you use a stylus!
Often the easiest way is to count your way along a row of sockets with the stripped end of the wire you’re planning to insert. Finally, you can most easily find the gap between upper and lower header sections with a fingernail, or by running the side of the probe along the edge of the header block.
Once again, my thanks to John Schimmel of DIY Ability, this time for transcribing the socket information off of a JPG and for providing awesome background links.