With modern understanding of pharmakinetics, researchers already have an idea of how drugs will act in mammals based on already understood compounds in or similar to the study drug. They can sometimes already tell what the half life is as well (this is how quickly the chemicals decay, or essentially stop working), so they know how long it will take for the drug to stop having an effect though it can behave differently in the body.

Study drugs are first administered to animals to determine potential AEs (adverse events, like side effects) and continue to study the half life by collecting blood and/or urine at specific intervals of time. Say they give the study drug at 8:00 am, they may draw blood or collect urine every 2 hours over the course of 12 hours. There will be less of the drug as time goes on, and they are using the blood/ urine samples to determine specifically how quickly it is passed though the body and how strong/ effective the medication is based on amount present in the sample.

Then they do the same thing in volunteer humans that get paid to be in a trial. They follow very strict procedures, the volunteers stay at the research facility 24/7 for a set period of time (could be a day could be 40 days) and are given the same food. The procedures (which includes when they administer the study drug or placebo, when they take blood or urine, when they take vital signs, EKG, weight, etc) are written out by the pharmaceutical company who developed the drug and are followed down to the second. Volunteers even need to pee at specified times. All adverse events (side effects) are recorded and there are usually follow up visits after the study volunteer is done with the initial stay to continue monitoring until the drug is no longer affecting them.

There are multiple arms of in-human studies where they do the same thing but with different diets, ethnicities, etc to see how the drug may be impacted by different factors.

So yes, they do a lot more than just blood testing and it is at very, very specific intervals of time. Usually vital signs, blood, urine, heart, etc are tested at specific times.