Installing a flush toilet in a tiny home is about the same as it is for a regular house. No one does DIY better then the people of, “This old house”. Here is their instruction video on how to install a new toilet.
If you are going to install a flush toilet in your tiny house, please consider going more eco-friendly and combine the sink and toilet tank. This will help you conserve water and give you more space in the bathroom by eliminating the need for a bathroom vanity.