The euphonium plays in both C and Bb.
The euphonium and French horn both have different transposition levels. The euphonium typically plays in C making it a non-transposing instrument. The French horn, however, is not a non-transposing instrument and sounds in F, which means the sound produced will be a perfect fifth lower than written. Because of this, if you were to give a French horn player euphonium music without transposing, the French horn would play the notes off by a fifth.
Instructions
1. Learn transpose up a perfect fifth. The perfect fifth consists of seven half steps. With this knowledge you can determine that a perfect fifth above Eb is Bb. While A# is also seven half steps above Bb, you would use A# because A is actually a fourth away from E.
2. Transpose every note from the euphonium part up a perfect fifth.
3. Determine whether the transposed part is within the range of the French horn. In most cases, this won't be a problem since the horn can play the entire range of the euphonium. However, if the part uses notes below E two octaves below middle C, you will have to transpose the music up an octave.