There are a number of ways.
One of the ways I have done this (over 6 decades of current, incidentally) is to put the load current path as the programming side of a current mirror.
The other side of the mirror will have the same current (within the tolerance of the device - see the ADI MAT-0x series for excellent matched mirrors, or perhaps choose a Wilson mirror - you should really only need this if you have large variations of programming current or supply voltage- a Wilson mirror is designed to negate Early effect, a variation of bipolar transistor gain proportional to Vce. Use one if the effective Vce of both sides of the mirror will differ significantly).
This output current may then be amplified, converted etc., to your heart's content for the measurement system.
Cheers PeteS