Hmm, it's time to start explaining why we care so much about these crazy sounding elements, uranium (U) and thorium (Th). Remember the periodic table in high school? Uranium and thorium are both large metallic elements near the bottom of the chart. For example, while oxygen weighs only about 16 units, uranium weight averages about 238 units and thorium 232 units! Most importantly- both these elements are also radioactive, which means that they decay at a certain KNOWN RATE over TIME.
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Ok, so just a quick lesson on how radioactive elements can be used to date a material: Each radioactive element decays over TIME at a given RATE (can be labeled as it's particular "half-life") that has already been scientifically determined. Let's say you have a pile of 1000 radioactive parent-blobs, whose "half-life" is known to be 7 days. That means that one week from now, about 500 parent-blobs will have decayed into daughter-blobs, while the other 500 parent-blobs are left in your pile. Two weeks from now, only 250 parent-blobs will be left. Three weeks from now, 125 left. If you were a scientist that walked into the room and saw 125 parent-blobs and 875 daughter-blobs, you'd know that to begin with there must have been 125+875=1000 parent-blobs, and you'd be able to calculate that 3 weeks had passed.
"U-series" dating is a bit more complicated because we are dealing with a chain of events (U-238 decays into U-234, which then decays into Th-230) but the idea is the same. What we need to know is how many U-238, U-234, and Th-230 atoms are present in our rock samples, and then using math equations we can calculate the exact age.
Ok, so now we can start! First step, get dressed to enter the wet chemistry super clean room. Ah, beautiful! :)