Screen printing:
Screen printed shirts are everywhere and are probably the most common method used. Screen printed items are used for shirts, towels, promotional products, etc. A majority of the t-shirts you see out in the marketplace are screen printed.
How it works:
A design is divided into layers, a screen is made for each color and then the garment is screened by color one after the other. Of course this is a simplified description of

Pros:
Screen printing is great for large runs of the same design (at least 36) and if there are minimal colors. T-shirts are the most commonly screen printed item, however polo shirts and totes may also be screen printed. The cost per item is usually lower when screen printed because of the larger run requirements.
Cons:
High setup cost . Setup charges are usually per screen per color per side. Larger runs required each time to make it economically worthwhile.
Heat Transfers:
There are many forms of heat transfers however the most common are vinyl and plastisol transfers.
How it works:
Designs are either cut from vinyl, screen printed on release paper or printed on transfer paper and then are heat pressed on a garment.

Pros:
Transfers are great for small runs, generally less than 36 pieces or when you want full-color or custom printed garments such as names and numbers. If printed on transfer paper, designs can be full-color, even a photograph. There are generally no setup fees for transfer printing. No minimum requirements.
Cons:
Higher cost per garment. Some transfers will only work on light garments.
Embr

Embroidery has the highest perceived value or quality out of all the embellishing methods. Embroidered apparel is seen nearly everywhere: banks, hotels, corporations, small businesses, gifts, etc.
How it works:
Stock embroidery fonts or designs are generally available however custom designs need to be digitized by a skilled digitizer using specialized software. Once a stitch file is created, it is inputted into a computerized embroidery machine and the design comes to life by using threads.
Pros:
Higher perceived value. Lower or no minimum requirements. Flexible, same design can be embroidery on different garments and products.
Cons:
Higher cost, digitizing fee, certain limitations on size and effects of the design.
Regardless of which method you choose, great results can be achieved if you ask the right questions. Hopefully, this little quick comparison of the different methods will help you in your decision making process.