I didn't have to take the MCT as an applicant as I had childhood exercise-induced asthma until I was 12. That met the DoDMERB standard. However, I did have to take one to get qualified to fly. I'm guessing you have taken a spirometry before. It is pretty much a series of spirometries given after increasing concentrations of methacholine, which is a bronchoconstrictor (a drug that makes your airways swell). The degree of broncoconstriction is measured by the decrease in FEV1 from the baseline measurement. FEV1 is Forced Expiratory Volume in 1 second. In layman's terms, it is the amount of air you exhale in one second.
As you alluded to earlier, a positive MCT (indicative of asthma) is a drop of greater than 20% in FEV1. A negative test (suggestive of not having asthma) is where the patient does not experience a drop greater than 20% FEV1 after receiving the highest concentrations. Doses are given in a stepwise manner (You start with no methacholine to get a baseline and then you are given a series of 4-5 doses of increasing concentration. I had 5 if I remember correctly). After the test, you are given albuterol and you take additional spirometries to ensure your airways are back to normal. Everyone will experience some drop in FEV1, but 20% is what is considered hyperresponsive.
My experience: I was pretty tired during in the latter part of the test since you are breathing out as hard as you can over and over. You most likely won't feel any chest tightness. My chest was actually kind of sore for a few days after, but I passed the test so I didn't mind. If you have been unrestricted asthma-wise, you shouldn't have any problems.