Studies of the low-mass population statistics in young clusters are the foundation for our understanding of the formation of low-mass stars and brown dwarfs. Robust low-mass populations can be obtained through near-infrared spectroscopy, which provides confirmation of the cool and young nature of member candidates. However, the spectroscopic analysis of these objects is often not performed in a uniform manner, and the assessment of youth generally relies on the visual inspection of youth features whose behavior is not well understood. We aim at building a method that efficiently identifies young low-mass stars and brown dwarfs from low-resolution near-infrared spectra, by studying gravity-sensitive features and their evolution with age. We built a dataset composed of all publicly available (~2800) near-infrared spectra of dwarfs with spectral types between M0 and L3. First, we investigate methods for the derivation of the spectral type and extinction using comparison to spectral templates, and various spectral indices. Then, we examine gravity-sensitive spectral indices and apply machine learning methods, in order to efficiently separate young (<~10Myr) objects from the field. Using a set of six spectral indices for spectral typing, including two newly defined ones (TLI-J and TLI-K), we are able to achieve a precision below 1 spectral subtype across the entire spectral type range. We define a new gravity-sensitive spectral index (TLI-g) that consistently separates young from field objects, showing a performance superior to other indices from the literature. Even better separation between the two classes can be achieved through machine learning methods which use the entire NIR spectra as an input. Moreover, we show that the H- and K-bands alone are enough for this purpose. Finally, we evaluate the relative importance of different spectral regions for gravity classification as returned by the machine learning models. We find that the H-band broad-band shape is the most relevant feature, followed by the FeH absorption bands at 1.2um and 1.24um and the KI doublet at 1.24.