Checking capacitor ESR with basic test gear
I have a couple of multimeters with AC millivolt ranges and forward reading resistance ranges. With one of these meters (a Unigor A43 and a Schlumberger/Weston 666, aka Heathkit IM-104, other suitable meters are available) connected to a function generator output, you can use the meter on its AC mV range and read ESR directly off the meter's resistance scale
You need to shunt the function generator output so that the overall impedance matches the centre scale reading of the multimeter Ohms scale (10 Ohms in my case).
Then set the function generator output level to give fsd on the multimeter with the shunt connected, but not the capacitor under test.
Connecting the capacitor will cause the reading to fall, for example, if the ESR is the same as the generator/shunt impedance, the reading will fall to half scale. With a standard non-linear Ohms scale, but forward reading (i.e. Zero Ohms at zero deflection, infinite ohms at FSD), then the capacitor ESR can be read directly from the Ohms scale (the meter still being set the AV mV).