So much to learn - so much fun!  The cups and stuff are typically sublimation, so check out that section.  Shirts can be many ways, often cut vinyl.  Google and read up on Siser brand Easyweed - really cool stuff!  Just when you think, aww this is easy - yup - look out (see my posts on trying to learn contour cutting).  This can be as deep a subject as you like.  Welcome, and enjoy!