Pianists have notorious difficulty in transposing instruments, simply because they never have to do it. However, a quick technique that uses the spatial visualization of the keyboard will turn this weak skill into a strong one.
Taking the French Horn example. The horn in F is in fact called the horn in F because when someone plays a middle C (that's given on their staff paper) on their instrument, a concert pitch F comes out. So logically, the concert F pitch is the horn's staff paper middle C.
*It's important to note that for most instruments, the concert pitch that comes out is the pitch below middle C, and not above, unless it's an octave transposing instrument like the cornet.
Method: The "Pinky-Thumb Method"
1) Visualize the keyboard in your head.
2) Put your pinky on the keyboard middle C (or for the purposes of the 2nd step, their staff paper middle C), and put your thumb on the concert pitch of the instrument.
Staff paper middle C = Pinky (Almost always, unless it's an octave transposing instrument)
Concert pitch = Thumb
So for the horn in F:
Middle C = Pinky
F below middle C = Thumb
3) Notate the interval in your head
In the case of the horn in F, the interval between the pinky and thumb is a perfect 5th.
4) You're Done.
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In your imagination, in the example, keep the perfect 5th interval consciously knowing that your thumb is the concert pitch, and the pinky the what they have in the staff paper. So for example, if you want a concert C to sound on the horn, you're going to have to write a G on their staff paper. You do the same for any other instrument. If you want the tenor horn for example (horn in E flat), then you just follow the same steps with the interval being a Major 6th instead of a perfect 5th.
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