They can be screen printed or be done with a heat press(like t-shirts) . Sometimes we screen them, other times we make transfers and press them, and still other times (very few) we use inkjet transfers. 
Linda, do you have a heat press? We use our regular 16X20 flat heat press, we don't have a hat or mug press. We sell high quality flat or the wrap around with neoprene koozies, customers will pay a bit more to have a better koozie. I have seen tons of koozies that are real thin and customers appreciate when they see samples we have made that the koozie is thicker. We use the JPSS paper with Epson Durabrite ink and they last! We buy in bulk so are able to give discounts for large orders, say is a customer orders 200-300 for a wedding, we will sell them for $2.50. Cost is less then $1.50 for us, we just made $200-$300 depending on how many they order. Just made up some samples for the local fire dept., they gave me one they had from another town, again it was thin! They loved the samples I made them and loved the quality of the koozie, they are deciding on how many to order between 36-48 selling them for [email protected] they think they are getting a great price ... I'm making [email protected] profit! We are from a small town of less then 5,000 people with volunteer fire dept.! Let me know if you have any other questions, I would be happy to help!
Jody