Below is a prototypical fundamentals routine based on exercises that I do every day in order to develop and maintain my trombone technique. I encourage you to check it out and steal whatever you like for your own use!
Check out these free materials on a daunting and often skipped-over topic in brass pedagogy. Doodle tonguing is not just for trombonists, not just for jazz players, and not as difficult as you may have been led to believe! Check out the videos below to hear some doodle tonguing in action, then download the solo PDFs to play along!