To transpose music is simply to write it in a different key. All the relationships between the notes remain the same. Notes that sound as written are not transposed away from the original key.
For some instruments, music is written in a different key from the original key, or concert key. These transposing instruments include the Trumpet and Clarinet, as well as the Tenor and Soprano Saxophones in Bb. They read music in a key one whole step higher than the concert key. If the concert key is B-flat major, their part is written in C major. Instruments pitched in B-flat all sound a step below written. The E-flat Alto Saxophone is transposed up a Major 6th, and the Horn in F is transposed up a Perfect 5th. Memorize this adage: