A mat file is created simply by saving a material when you are in the material editor. Just click on the floppy disk button on the dialog box and save it. You then have a file which you can load afterwards.

To apply a jpg (or other format) as texture you have to go to advanced material editor, tab "color & alpha", click on "mapped picture", click on the little yellow arrow below the black square that will appear and point to the image file you want.

These are really basic questions so I highly recommend that you read the manual... :-) You are surely missing many other important things.