How do you determine the amount of acrylamide in foods such as baked fries?
Check out the methodology page for the FDA section on acrylamide quantitation, which goes into considerable detail.

In short, they start by mashing up some fries, and then extract and purify a fraction containing the acrylamide through a number of steps leading up to liquid chromatography. They then use quantitative mass spectrometry to determine the amount of acrylamide present.

They add a small known concentration of isotopically labelled acrylamide (i.e. acrylamide with all the carbons as carbon-13, which has very low natural abundance and results in a molecule that is approximately 3 g/mol heavier). This shows up in the mass spectrum as an offset peak. Then they can integrate the normal acrylamide mass spectrum peak and the labelled peak and obtain the concentration from the relative peak areas.