1) create a new destination sample buffer (you will want to know the sizes).
2) read the samples (e.g. using AudioFile and ExtAudioFile APIs) and write them in sequence to the buffer. You may want to add silence between the files.
It will help if your files are all the same bit depth (the destination bit depth - 16 should be fine) and sample rate.
Alternatively, if you have fixed, known, sample rates and bit depths for all files, you could just save them as raw sample data and be done in much less time because you could simply append the data as is without writing all the extra audio file reading programs.