MFCC classification model
When utilizing MFCCs, it is common to split the MFCC matrix into pieces. Lets assume your MFCC-matrix $\bf{M}$ has the dimensions $[\bf{M}]$$=N \times 39$, where $N$ denotes your time index and you have 39 MFCC bins. Then you cut your matrix into blocks of length $B$ (I propose $B=39$ so your blocks have a square shape) and save them in a list. For the last block, you can either zero-pad until it has the same length or discard it completely. Each block has to be annotated with the label of the original audio sample.

A standard approach for classification is a Deep Neural Network, that consists of Convolutional and adjacent Pooling layer since MFCCs are like images locally connected/correlated and Convolutional layers take care of that. Of course, you should not forget to add an MLP layer at the end with a softmax activation to get an estimated probability distribution as an output of your net as well as an appropriate regularization technique.

A more advanced approach would be the use of a recurrent network structure like an LSTM-gate or a plain Recurrent layer. Therefor, you have to store the blocks of a sample in chronological order so the network can learn the temporal structure of a whole sample.

EDIT: Actually one often takes only 13 MFCC bins. The $N \times 39$ matrix also contains the Deltas and DeltaDeltas of the MFCC bins.