Embroidery is thread sewn into the garment to make up the artwork.  It is the most durable option and adds texture.  Screen printing is printed by first separating the artwork by color.  This method is good for simple artwork that is less than 6 colors.  Transfer printing is the design printed on a sheet and then transfered to the garment with heat.  This is good for artwork that is more complicated with lots of colors and detail.