A good way to try learn to play a double-trigger-bass-trombone is to warm up or practice playing different notes by checking out information and guidelines on how to play via website http://www.wwbw.com/Double-Trigger-Bass-Trombones.wwbw
Listen to professional trombonists, listening to a professional will give you an idea of what you can sound like on the trombone. Listen to CD’s, take some inspirations, listen to great musicians.
Make sure you practice your scales every day, it will help with your embouchure control. Playing long tones, for example, holding one note for a long time, does two good things: 1) It will improve your tone. 2) by having to sit on one note, you will learn how to control your airflow. Ideally, you will have a constant flow of air.
Keep the instrument in a playable condition; clean the inner slide off and re-cream/re-oil it weekly, bathe the bell section (yes, bathe, with lukewarm water and some detergent), grease the tuning slide at the top with petroleum jelly or “slide grease”, they’re both petroleum jelly, and if there is a valve, oil it with the appropriate valve oil.
Join a beginners musician club or take private lessons with a tutor. It will take years for most people to play a trombone well. Practice! Every day for at least 30 minutes, or about 210 minutes all week. Try to spread it out, and schedule it in a way that won’t drain you, but if you feel you need to do a lot on one day that’s fine, if you can do more, the better!