Maybe your band director or private lesson teacher has mentioned the word vibrato before, saying that you should use it while you play a solo. When used right, vibrato can make even the most thick hearted get a lump in their throat. Vibrato in itself is really quite easy to do, it is trying to master it that most people give up on. There are three types of vibrato that trumpet players use: lip, diaphragm, and hand. .
Hand vibrato can be used in all types of playing and is easy to turn on and off as you play. To do it, all it takes is for you to lightly "rock" the horn in circles as you hold out long notes. What speed you do it at is determined by the style of music playing. Usually music that is in mariachi style requires a fast vibrato while music that was written during the Classical era requires a slower, more drawn out vibrato. Further information on this can be found in Musicality and Phrasing.
Lip vibrato is not all that much more difficult to do than hand vibrato, it just takes more maturity to execute. Lip vibrato is preformed by moving your mouth in a "chewing" fashion while you hold out longer notes in a piece. While it may sound easy, it takes a mature player to do this and not make listeners think they are drunk. Lip vibrato should only be used in jazz and symphonic styles of music. I would not suggest that you use it in styles like mariachi. In what style and where to use lip vibrato is discussed more in depth in Musicality and Phrasing as well.
Diaphragm vibrato works on much the same premise as lip vibrato, but you move your diaphragm, the muscles below your lungs, to vary the air supply instead of moving the lips.