Transposition

From Clement's:

It can be confusing to remember which way to transpose: up or down?

A simple way to remember is to imagine the transposing instrument playing a C major scale that you've written out.  This will sound the same as the major scale that the instrument is "in", e.g. it will sound like B flat major when played by an instrument "in B flat". Therefore by writing out a C major scale, you have effectively transposed a B flat major scale for an instrument "in B flat", by transposing it a major 2nd (from B flat to C). If you want to know what note a C written for an instrument "in B flat" will sound as, it's the same as the name of the instrument: so B flat in this case.

Similarly, a French horn in F playing a written C major scale will sound as the scale of F major a perfect fifth below the C major scale you've written: so you transpose up a perfect 5th to write for a French horn in F. Therefore, if you want a French horn to play an F, you would write a C; if you want them to play a G, you write D, and so on. Conversely, to find the pitches that would sound from some music written for a French horn, you would transpose by a perfect fifth: a written C sounds as F, and a written D sounds as G, and so on.