The degree of saturation of a nitro group, -NO2, is one.
Nitroalkanes show two NO stretching vibrations near 1550 (asymmetric) and 1365 (symmetric). Nitro-aromatic compounds show two similiar bands, but shifted to lower frequencies: NO stretching vibrations from 1550-1475 (asymmetric) and 1360-1290 (symmetric). These bands are in areas that overlap with other functional groups and therefore may be hard to attribute solely to nitro groups.
The proton adjacent to a nitro group shows up from 44.4 ppm.