- V-I: Dominant - tonic: authentic or perfect cadence.
- IV-V-I: Subdominant (or predominant) - dominant - tonic: another (fuller) authentic cadence.
- ii-V-I: Supertonic (or predominant) - dominant - tonic: yet another authentic cadence.
- II (V/V)-V-I: Dominant of the dominant - dominant - tonic: (you guessed it) yet another authentic cadence.
- IV-V: Subdominant (predominant) - dominant: half or imperfect cadence.
- ii-V: Supertonic (predominant) - dominant: another half cadence.
- V-vi: Dominant - submediant (tonic substitute): deceptive or interrupted cadence.
- IV-I: Subdominant - tonic: plagal cadence.
- iv6-V (- I): Subdominant minor (predominant) - dominant (- tonic): Phrygian half cadence (authentic cadence).
- It+6/Fr+6/Gr+6 - V (- I): Augmented sixth (predominant) - dominant (- tonic): Half cadence (authentic cadence).
You can substitute iv for IV, i for I and VI for vi, depending on mode, for most of these cases. I didn't list II-V as a half cadence, although it can make a perfectly valid one, because there is a fair potential for ambiguity: is it II-V in the tonic key or V-I in the key of the dominant? This will be context-dependent, and you will find that you will need to refer to the context when teaching.
This list is by no means exhaustive (it misses the Neapolitan sixth as a predominant, for instance), but it does give some insight into how function factors into cadences: cadences tend to fall into some variety of half, authentic, deceptive or plagal, and the functions of the chords involved tend to be some variety of subdominant (or substitute), dominant (or substitute, e.g., vii°) or tonic (or substitute).
It is sometimes simpler to refer to a chord that leads into the dominant as a predominant, because they will sometimes partake of mixed function. V of V, for instance, is almost a "super-dominant", and the French sixth combines a gapped dominant seventh of the dominant over a descending leading tone bass (♭6 moving to 5), so works both as a dominant and a subdominant. (Augmented sixths can act as dominant substitutes as well as predominants. I would contend that jazz tritone dominant substitutions are really just mixed function augmented sixths.)
In a modal context, using v as a dominant is a bit rare (due to the fact that, without the leading tone, v doesn't much sound like a dominant). Plagal (iv-i, Iv-i, iv-I and IV-I) and plagal-like cadences involving ♭VII6 or ♭vii6 are going to be common in modes lacking V. In Pop music, where parallels are not necessarily a consideration, you may find ♭II or ♭ii used in plagal-style cadences as well. Half cadences in very minor modes like the Phrygian will tend to move to the subdominant as well (e.g., i-iv).