Molecular assays are tests for the presence of particular molecule.
Molecular techniques can be assays or other manipulations, such as restricting (cutting) and ligating (pasting) DNA.
Some examples of molecular assays useful in detecting infectious disease include:
polymerase chain reaction (PCR)
enzyme-linked immunosorbant assay (ELISA)
Wikipedia is generally a good starting place to read some background on these sorts of assays (http://www.wikipedia.org).