Actually, if you do just that you will get some accidentals wrong.

To transpose correctly from one key to another, all notes must move the same number of semitones.

To transpose from C Major to D Major, for example, you step up 2 semitones. All other examples are just an expansion on this method.

Write out both scales, the original one on top, and the new one underneath, note for note. Take each note of the tune and go from top to bottom. You write the new staff notation and write the transposed tune thereon.

If you are transposing Minor Keys (or other modes), you do the staff notation, and as you add a note, you add the accidental if it is needed.

Robin