Transposing

The trumpet is a transposing instrument, in Bb. Quite often music is also written for trumpet in C, D, Eb and F. With practise it is possible to transpose into all of these keys.

C Transposition 
This is the most common transposition and probably the easiest.
Trumpet in C to Trumpet in Bb = up a tone.
Adding two sharps to the key signature will give you the new one. (for example C major will become D major, F major will become G major).

Trumpet in C

Trumpet in Bb

Eb Transposition
Trumpet in Eb to Trumpet in Bb = up a perfect 4th
To work out the key signature at one flat (G major-C major etc.)

Trumpet in Eb

Trumpet in  Bb

F Transposition
Trumpet in F to Trumpet in Bb = up a perfect 5th.
To get the key signature add one sharp.

Trumpet in F

Trumpet in Bb

D Transposition
Trumpet in D to Trumpet in Bb = up a major third
To get the key signature add four sharps.

Trumpet in D

Trumpet in Bb

I would recommend using a sight reading book to practise transposition to different keys. As you get better, move onto exercises that are the next level/grade up.