We realise that we cannot always be there to help you progress, so here are some very useful links to YouTube and some other resources in the public domain.
It is not necessary to purchase any of the books mentioned here as it is often easier to read from the computer screen, and pdfs do not get torn and dog-eared!
Trumpet Lessons from BasicBand.info
This series of videos is designed for the very basic player, starting from scratch.
I recommend it to everyone of all abilities, it may well tell you something you did not know or had forgotten.
BasicBand trumpet method book for beginners (pdf format).
This video shows a very good way to warm up your instrument and your lips! The notes played here include the lowest notes normally used on the instrument. Playing these notes is good for developing the muscles in the face and assists greatly when you are a more advanced student looking for the higher notes!
Practice at different speeds, (YouTube has custom playback in the settings section).
First Book of Practical Studies for Cornet and Trumpet by Robert W Getchell
This First Book of Practical Studies is designed to develop chord consciousness, to provide additional experience in the fundamental rhythms, key signatures, articulations, and improve accuracy in reading through the use of interesting and melodic studies. It may be used either to supplement or to follow any beginning method book.
Herbert L. Clarke Elementary Studies
This fine method by the legendary cornet/trumpet player. Herbert L. Clarke, contains some great advice and hints from an undoubted master, to aid the aspiring trumpet or cornet player with the various lessons through the book.
The Complete Arban Method Book - YouTube
In the Introduction, J. B. Arban covers the range of the cornet (trumpet). He also details alternate fingerings and describes the use of the tuning slide. Arban states his opinion that the mouthpiece should be two thirds on the lower lip and one third on the upper. (Herbert Lincoln Clarke recommends the mouthpiece to rest half on the upper lip and half on the lower lip). Arban then stresses the proper "attack" technique. He uses the "tu" pronunciation, in contrast with modern teaching, which often uses "tee". Arban concludes with proper breathing techniques. Continued.