Trumpets are one of the more easily self-teachable instruments (especially if compared to something like the violin), so by all means go for it. Someone mentioned the Rubank books, which are quality beginner method books. Standard of Excellence is another option.
If you find yourself staying with the trumpet for some time, invest in a copy of the Arban's book, which has been referred to as the trumpeter's Bible. It starts with basic and simple exercises, and ends with The Carnival of Venice.
It's been done many times before. Helps if you can read music and already play another instrument. Get a beginners music book to learn the fingerings.
Anyone who plays a brass instrument can show you how to vibrate your lips into the mouthpiece to produce a sound. Practice will make the sound better as your lips get stronger. Most important .
. . Have fun!
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