There are many commerical instruments that can go well below a pA
See e.g.
http://www.keithley.com/products/dcac/sensitive/lowcurrent/?mn=6485
This is from the point of view of the user no different than using a multimeter.
Note that how well you can do this will depend on the impedance, it is possible to measure very small currents if you somehow can "translate" your current into a voltage via a (large) impedance (but there are limits to how this can be done, e.g. the Johnson noise of the impedance).