How does drug testing work?

I'm curious how the actual drug testing works. The reason i ask is because I do these studies that pays me and all i have to do is take a marketed drug and give blood every so often and urine test's once in a while. Of course the purpose for those isnt for drug testing its to see what effects the drug has on your body, so i'm just wondering if they probably werent looking for something like thc would they find it? Is it something they have to specifically look for or is it gonna be noticable somehow just by doing whatever tests they do? I"m sure they look at certain aspects of my blood and urine and such but would it tell them anything about marijuana use if they were not specifically looking for it. They do a screening before you can get in the study and thats when they do drug screening and such, so i've already done that and passed fine. Now i'm just wondering during the study if they would maybe notice it even if they wernet looking for it. Hopefully this makes sense. Thanks