When most students think of trumpets, they are thinking about a Bb trumpet, which is by far the most popular trumpet in North America. A Bb trumpet is the standard in bands and in jazz ensembles, due to it's warm tone and good response. A Bb trumpet is almost always the first trumpet used by trumpet players in the US. This trumpet is called a "B flat" because it is tuned to the key of Bb, meaning that the first note in its harmonic series is a concert pitch Bb. If you look at the note on paper, though, it is written as a "C." Why? This is done so that new fingering patterns do not have to be learned when switching to an instument of a different key, like going from playing a Bb trumpet to a C trumpet.
Example: If you play a C on a Bb trumpet, it will sound like a Bb to the band and to the tuner.
Think about it-- a concert C would be a harmonic (played with open valves) on a C trumpet, but played with the first and third valves down on a Bb. Confusing? Definitely. It takes a straight head to reason this out.
This can be a problem, because a Bb trumpet player can not read piano, voice, or string music (which is said to be written in "concert pitch" ) and and have it sound the key that is written. The trumpet player must "transpose" the music into the same key. To read music in "concert pitch," a Bb trumpet player must play every note one step higher than what is written. This is done by removing two flats (or adding two sharps, as the case may be) to the key signature and then reading the notes as if they were one line higher.
Don't worry about this too much if you are just starting to play, because most printed music for trumpet has already been transposed for you, so you may play the music as written. You will know your music is transposed if at the very top left hand corner it reads "Bb Trumpet." If it says otherwise, check out the part to make sure by comparing the key signature to a concert pitch instrument, such as a flute or trombone.
Transposition becomes a problem when you are playing a piano part, or backing up a choir on a Bb trumpet. The most common transposition that is required of trumpet players still in junior high or high school is transposing just one note that your director may ask for. Many bands, for instance, will tune to a "concert F." To play it, just move up one whole step in the musical alphabet to the note "G." This is relatively easy to do. Just remember: a whole step up from Eb is F, and a whole step up from B is C#, because there is no E#/Fb or B#/Cb. Because of the problem of transposition, many trumpet players will play a piece that requires transposition to concert pitch on a C trumpet, which eliminates the need to transpose. Most present day professional trumpet players play all their pieces on a C trumpet though.