"Fewer" means "a smaller number of something", so use it for anything you can attach numbers to.
"Fewer samples were taken from site B than from site A (12 vs.15)."
"In the treatment group, fewer mice exhibited symptoms than in the control group (25 vs. 38; Table 1)."
Use "less" if you're not referring to individuals you can count, but rather to a decrease in a particular quality or concept.
"We had less success in raising viable embryos using this technique."
"We observed less change over time in group A than in group B."
The same rules also apply to "few" vs. "little", e.g.,
"Few of the incubated samples displayed fungal growth." (Few samples of many potential samples)
"We observed little growth in the experimental group." (Growth is the quality being observed, not something to be counted.)
Still confused? Put your questions in the comments!