Reddit mentions of Arbans Complete Method: Trumpet, Platinum Edition (Book & CD)

Get these books; I wish I had them when I first started. They work in synergy, developing your tone, range, lip flexibility, and finger speed tremendously.

Systematic Approach to Daily Practice: I call this my "flagship" book because it tells when and how to use the other two books, as well as provide its own tone-and-range-work.

Clarke's Technical Studies: Develops finger speed and endurance.

Walter Smith's Lip Flexibilities: Develops range and lip speed.

And, lastly, a book not normally part of the Systematic Approach,
A Physical Approach to Playing Trumpet: Posture, breathing, hand position, embouchure, etc.

I'm not an expert on trumpet or anything by a longshot, but these books helped me tremendously.

Oh, I almost forgot: Arban's. Basically the Bible of trumpets.

I highly suggest you buy the platinum version. It has spiral rings that allow for the pages to easily turn and STAY turned (and that makes a BIG deal if you tend to get angry during practice like I'm sure most of us do)

The prices I saw in this entry are extravagant save for the $34 "collectible"; you may as well buy it at a music retailer for ~$50.

Trumpet takes a long time to learn how to play well, but picking it up is not terribly difficult. The biggest problem you'll notice when you start is the finesse it takes to play high notes. It uses muscles that you've probably never used before and It will take a while for you to even be able to play one octave.

Rubank Elementary method is a good place to start. Then move on to Intermediate. http://www.hornplace.com/BB038.html .

Once you have those under your belt, Arban's is the trumpet bible http://www.amazon.com/Arbans-Complete-Method-Trumpet-Platinum/dp/0825858526 . That book will keep you busy for a lifetime.

If you ever need help or have questions, feel free to message me.