How is an accelerometer initially calibrated?
It is possible to use gravity to calibrate an accelerometer but it has drawbacks.

Typically, for any accelerometer the Bias and Scale factor are calibrated. In this case the accelerometer output is measured in the +1 and -1 g positions, that is, measuring up and down. The average of those measurements is the bias, and the scale factor (in units of output per g, or typically mV/g or mA/g) is the average of the absolute value of those results.

This method has some drawbacks. First, if the scale factor is large, say 1000 g Full Scale, then you are only exciting .1% of full scale. You can imagine that this may not be the most accurate way of doing things. If there is non-linearity in the output, then this method will not measure it well.

For example, if there is 1% non linearity, meaning the maximum deviation from a best line fit is 1%, typically happening at full scale, with a 1g excitation, only 1% of .1% or .001% deviation is measured, and this could be missed in the noise. 

The Earths' gravity is not constant around the planet, and for very sensitive accelerometers, some allowance for this must be made. In fact, there are accelerometers which are so sensitive that they will measure the passage of the moon around the earth.

It would also be critical that the "1 g flip" as it is called, is truly taken over 180 degrees. Any error from that will cause an error in the calibration.

Finally, while some accelerometers respond to a DC input, for example, capacitive, open loop MEMS accelerometers, not all accelerometers do. Typical examples of these are piezoelectric accelerometers, which only respond to higher frequency inputs. So the 1-g flip calibration can not be used for these.

Having said that, in the field, a simple 1-g flip is a very useful tool to determine if the accel is functioning right. You basically have a universal cal standard around.

The other method which is typically used to calibrate accelerometers at the factory is a "shaker". In this method, the accelerometer is mounted to a fixture which can apply a sinusoidal motion. The accel is then shook at various frequencies and amplitudes. From the output data the scale factor, bias, non-linearity, and other parameters can be measured. The accelerometer can then be calibrated. Typically the accelerometer will have non-volatile memory on-chip which will accept calibration values. The ASIC which reads the physical signal and converts it into a useful output will often have the ability to modify the output by the calibration values, adjusting the bias and SF and sometimes linearity and even higher order terms. The goal is to produce an output proportional to input acceleration only with no bias, etc.

The shaker itself contains a "calibrated" reference accelerometer which in tern is used the determine what the "true" input acceleration is. Those accelerometers are NIST traceable, or calibrated by NIST or a standards testing lab.

These are the two ways that I know of. There must be others.

For a standard reference try IEEE 1293-1998.