The diagnosis is mostly done by indirect means and by testing if the antidote does anything. Chronic mercury poisoning is very hard to diagnose by testing because there is no way to measure how much mercury is stored in your body except by cutting off pieces from various organs and sending them to a lab - obviously not feasible. There is the chelation challenge method, for example the "DMPS test", where you are given a dose of the chelator and then they check urine for heavy metals. The problem is most chelators only work in extracellular space. There are studies showing positive results of such a test do correlate well with heavy metal intoxication. Here is a summary paper from a lab - sorry, German: http://www.labor-bayer.de/publikationen/11_DrBayer-DMPS-2008...
You can also look at indirect indicators, for example my WBC count was quite low (and no clear reason presented itself) and a few other values were a bit wacky too.

Anyway, as for myself I was "lucky", I had elevated mercury levels in urine and in blood. I had hair tested too and mercury was very high. Since it's unlikely mercury in hair came from an outside source that directly (i.e. not through your body) contaminated the hair sample it can give a good indication that the person was exposed to mercury - it doesn't tell you anything about how much is in the body. After all, if it's in the hair it's a good sign because it's being excreted. Also, different labs may very well give you different results when you send them hair taken from the same person at the same point in time - this has been tested. What works better than trying to interpret an individual lab test is a trend: Take the same test each year - using the same lab of course - and look at the change. And always in the larger context, any single value of anything is rarely meaningful just by itself.

So after an initial diagnosis what completes a diagnosis is to start a probationary treatment with the appropriate chelator and see what happens. That's not unusual, a lot of treatments prescribed by your doctor are of that kind. Assume a diagnosis and test it by treating for the diagnosis.

This all goes into the much larger issue that we are far from knowing the effects of levels of chemicals
a) individually at low doses that don't show an immediate effect
b) cocktails of several substances at low doses.
We know quite a bit about effects of substances on a molecular and sometimes on a cellular level, but that doesn't translate well to knowing what happens long-term and at doses that don't have a clear immediate effect in real life. I can't find the reference any more, but a few years ago I read a study of LD50 values (lethal dose - it is the amount of the substance required to kill 50% of the test population, rats for example). They found that when you combine lead and mercury the lethality if about a thousand times higher than each one by itself. So of what use are individual legal limits? Their main purpose isn't medical but administrative, at what point is the cutoff point for effort vs. effect, e.g. money spend on getting the last bit of lead out of pipes and houses vs. beneficial effect. How long did it take for lead to be taken seriously? That was a lone fight for a long time, today consensus is - and I quote a professor of public health from a course on water treatment I took who presented the studies - that there is no known safe lower limit. Doesn't mean we can get to zero everywhere, so we do have an official limit for good reasons. I always cringe when people use those limits as arguments in a health debate though as if they were some sort of objective proof that there is no problem and anyone expressing concern is a tinfoil hat person.