Silk screen printing can be a great way to make the t-shirts you design and sell online.
You can make them yourself with an inexpensive starter kit. See screenprinting.com for an example of a company that sells everything you need to print your own t-shirts.
The site also has a great series of resources on learning screen printing including videos, online classes, and other resources:
DIY is a great approach for the hobbyist.
However, there are a large number of companies that can print your designs for you. One nationwide company that has a facility in Indianapolis is Underground Printing.