How do you do it? Although there are a few methods for transposing, one of the simplest is this:
1. You need to know the key signatures of the original key and it's scale degrees.
2. You need to know the key signatures and scale degrees of the destination key.
3. Then keeping the original scale degrees in mind, simply transfer them to the new key.
One time I was playing the famous C major two-part invention by Bach (BWV 772) and thought it would be fun to transpose it to a few other keys. Here is what happened:
Original in C major
Transposed to G major (a perfect fourth downward)
Transposed to F major (a perfect fifth downward)
In the above videos I play from the facsimile of Bach's handwriting - the right hand part is written in the soprano C clef (treble C is on the first line).
Would you like to learn transposing like that?