Shirts can be done in a variety of methods.
Silk screen printing is detailed and done with paint. This method allows for a stencil to be created, which can be used multiple times.
Vinyl iron on method has become the common way to make lots of shirts, quick. The use of a cricut machine helps to make many different patterns, but can be limited to the colours of vinyl that is available. Line art is common with this method and can be applied to almost any material.
Sublimation is a method that allows for a more detailed image with the use of a sublimation printer. Things like art work and photos are done well with this method, but can be limited to the materials it will transfer onto. For materials that cannot be directly sublimated on, a special material (like vinyl) can be used to put your image onto first, then it can be applied to any material.