Play a musical passage in the normal fashion by articulating every note with your tongue. This is the normal method of playing when there is no slur indicated.
Play the same musical passage, but keep your tongue lying flat against the bottom of your mouth. This produces a slur with the trumpet. Slurs involve playing the notes without the use of the tongue. It is as simple as letting your tongue rest. At first, this may be difficult, but with practice, it becomes easier to relax your tongue.
Practice scales and arpeggios by slurring instead of using the tongue to articulate notes. Pay special attention to your fingers, and practice getting a smooth sound between the notes. A smooth sound is obtained by quickly moving the fingers and synchronizing them with the other fingers. If you notice a break between the notes, practice slowly and concentrate on moving your fingers quickly enough to create a smooth transition between the notes.