This resource provides two approaches to teaching secondary dominant chords that are appropriate for high school AP students, liberal arts college non-music-majors, music minors, or music majors.
The first and most common way to spell secondary dominants is to think in the secondary key (with its concomitant sharps or flats), spelling the dominant chord in that secondary key, and then adding the necessary accidentals to have that chord fit in the primary key. For example, if one wants to spell a V/V in C major, one first has to determine the key of V (G), its key signature (one sharp), and its dominant chord (D). To notate that in C major, one then has to add an F# to the chord. As keys with more sharps or flats are introduced, this mental juggling of keys and key signatures can become more difficult.
One alternative and complementary approach to teaching secondary dominants is to construct them as altered diatonic chords through the circle of fifths. Almost any chord in the circle of fifths can be altered to become a major triad or a Mm7 chord, and thereby become the dominant of the chord that follows it.
This teaching resource provides a detailed explanation of this topic, and includes a number of worksheets from which instructors can pick and choose according to their students' needs. Instructors can also create more exercises following any of these models as they feel appropriate.