The trumpet is a musical instrument with the highest register (or range) in the brass family, and music for it is always written in the treble clef. If you know the basics of music theory, learning how to read notes for the trumpet will be easy. If not, you can still learn by reading the instructions below and slowly sounding your way through various notes and scales.
Familiarise yourself with what sheet music looks like: five lines on top of each other. The symbol on the left means that you're reading music in the treble clef, which will be common to all trumpet music. The two "4's" on top of each other are called the time signature. The top 4 indicates that there will be four beats per measure (sort of a musical sentence), and the bottom 4 indicates that a crotchet constitutes one beat.
Familiarise yourself with different types of musical notes. Notes look different depending on how long they are held. A whole note (far right) is an open circle, and in 4/4 time it is held for four beats. A half note (centre) is an open circle with a line standing up vertically on the end of it, and it is held for two beats. A crotchet (the first two notes on the left) looks like a half note except the circle is filled in; it is held for one beat. An eighth note looks like a crotchet, except it has a little "tail" on the end of its line and is held for a half of a beat. A vertical line separating notes signifies a measure break, and two vertical lines signify the end of the piece. Thus this picture is of a musical piece that consists of two measures. Because it's in 4/4 time, you'll notice each measure consists of four beats total.
Now you know different lengths of notes, but how do you know which notes they are? Notes are named from the letters A through G. This picture shows a simple C Major scale. The first note on the bottom is called the middle C; from left to right, the notes ascend to D, E, F, G, A, B, and finally C again. To play them, blow into the mouthpiece while using the correct fingering. To memorise which notes use which fingering, you'll need to consult a fingering chart (see Resources). In general, tightening your lips produces higher notes, while loosening your lips produces lower notes.
Playing the C scale, each note is a full step apart from each other. But other notes, called sharps and flats, exist between these full steps. A sharp is a half step above a note, while a flat is a half step below a note. For example, a C sharp is a half-step above a C and a half-step below a D. A D flat is the same thing as a C sharp. There are two exceptions: There's no such thing as a B sharp or a C flat, and there's no such thing as an E sharp or an F flat. Sharps are indicated by the pound sign (#), while the sign for flats looks like a lower case "b."
As with all instruments, practice, practice, practice. With the help of a fingering chart, play the C major scale and experiment with different lengths of notes, keeping a consistent beat and figuring out how high or low you can go. Eventually you will be able to play arranged music, read music in different keys or even write your own music.