Conventional way to measure Li-Ion cell capacity?
The cell capacity is dependent on the charge voltage, the discharge rate, and the end point voltage. The charge voltage and end point voltage also affect the cell lifetime.

This means there is no one 'right' way to measure the capacity of a cell, as both lifetime and capacity are desirable, but are in conflict.

Generally, what the people responsible for the headlines describing the cell will do is state the capacity using a charge/discharge regime that will result in short lifetime, and then state a lifetime 'up to' some much larger number of cycles that can only be achieved when delivering half that capacity. But such is specmanship!

You have to decide whether you want long lifetime, or best capacity, or a compromise, set your charge voltage and endpoints, decide on a discharge rate, and measure to those.

Let's look at this 18650A data sheet from Panasonic. They are a big name reputable manufacturer, and to their credit they tell you what conditions they have used, and quote their cycle lifetime under the same conditions that they quote the capacity. 

They charge the cells at 0.5C. That's slower than most commercial chargers, and results in an improvement in capacity. The endpoint voltage is the normal 4.20V. Their charge endpoint current is C/50, which is a longer charge than usual, most chargers will cut off at C/20 or C/30. The discharge is to an endpoint of 2.5v. I don't know of any commercial battery control systems that would take it this low, 2.7v to 3v is the norm.

The three extreme conditions means that you won't see the capacity they quote when using normal commercial charge/discharge controls with faster charge and more conservative endpoints. But you should if you replicate their conditions.