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Yes its very possible. Screen print is useful if you want to make many shirts. If you want to do a few, then heat transfer might be a better option. The set up is the hard part. After the set up though, it's a snap; providing you have all of the equipment.
The screens takes some time for preparation in cleaning and loading the screens with emulsion,
Then exposing the screen to UV light with your design to create the image on the screen.
Then washing out the unexposed emulsion and drying.
Apply the screen to press, then the ink. This is for one color. If you want to do more then one color, it would require a press that can handle multi colors.
Here is a link that talks about the process.
I hope this helps in answering your question?