Initially t-shirt printing is a process that is quite tedious if you do not have the right equipment, and it was still pretty boring even if you have the right equipment, back in the days when printing was known but there are many shops and websites that exist today that will take care of all your printing needs so that you get the message / logo that you need in professional quality without much trouble.
With custom printed t-shirt, you choose the color of your t-shirt; then you select the text that you want on the shirt (if you want) and the font you want to use. In order to know about designer T-shirt you can make an online search.
Image Source: Google
Furthermore you can select the graphics you want on the shirt; most sites will have pre-existing graphics you can browse and use if you want or you can create your own custom graphics and choose that for your custom shirt. Then setup a shirt as you wish, decide where each element will go and finally, send your design to a printing service that will print your design and send to your shirt.
It will be up to you to decide whether you want your shirt screen printed or embroidered.
With embroidery, custom graphics you must first be digitized by an expert so that the embroidery machine can read your design and reproduce it; fees for embroidery can be a bit like you are charged per stitch. So of course the bigger picture, the stitches will be required to complete and will be more expensive shirt.