The process is generally composed of two steps. First, the classifier learns how to discriminate between experimental conditions from the activity of each voxel and derives a linear decision boundary that separates classes. This is the training stage in a subset of data, during which weights associated to single voxels are adjusted to maximize how well the boundary separates the conditions. The testing stage is carried out on the remain data where the weights are used to calculate a weighted sum of voxel activity, which is compared against the boundary to guess the class. 
Thanks to high-resolution fMRI, and to the method described above, it is today possible to test for more complex predictions and to run very informative exploratory analysis that overcome limitations of univariate analysis. On one hand, MVPA can be used to investigate representation across widely distributed areas (Haxby et al., 2001). In a prominent paper, Barany and colleagues (2014) used MVPA to disentangle the relationship between areas involved in sensorimotor transformation. In particular, they aimed to find where, in the fronto-parietal network, sensory inputs are transformed into motor commands. This network is made out of quite distributed area and includes parietal regions, premotor cortex and primary motor cortex. To look out for candidates of sensorimotor transformation, authors assumed that suitable loci where those containing both input and output features of the ongoing transformation. Operationally they investigated which loci reflect interaction between pairs of features, or which one carried information about those pairs. This type of quest is not feasible with neurophysiological measurements (because recordings are circumscribed to specific small regions) or classical fMRI analysis (not sensitive to regional differences). Participants performed a set of wrist movements that differed along several aspects (target location, movement direction, movement amplitude, wrist orientation, and wrist angle). They hypothesized that the activity evoked by each feature’s neural representation would contribute differentially to the classifier output. Results provided evidence indicating superior parietal lobule as a locus in the transformation between target location and movement direction and showing that posture-dependent representations are widespread through the motor system. On the other hand, talking about exploratory analysis is worth to mention the multivariate searchlight approach (Kriegeskorte et al., 2006). This method allows to detect which regions contain information about experimental condition by mapping the entire brain. This is one of its most appealing aspects because it requires no a priori region specification. To build the whole-brain map of the most informative voxels, the idea is to run a series of multivariate “searchlight” analysis throughout the measured volume. A sphere of n-voxels radius is centered on each voxel, and for each of them multivariate pattern classification is performed.