"Hello there! Don't cringe now, I'm not really quite that loud, now am I? OHOHOHOHO!
The name is Vernon, and I am quite a friendly man. I could be considered a chocolate connoisseur, a cocoa aficionado if you will! And I believe I have a proposition for you that may make both of us happy. Before I gained my sweet tooth, I was a knowledgeable young lad who studied hard throughout university on Pokémon. I specialized in their move sets and have the skill to teach your Pokémon special moves that they wouldn't learn otherwise!
There are some wonderful chocolates from Unova known as Heart Sweets that I particularly enjoy. If you so happen to obtain any during your travels, return to me and I shall teach something special to your Pokémon.
Different moves may be easier or more difficult to teach, so be sure to stock up before paying me a visit! And you must make sure your pokémon are compatible with the move you would like me to teach them so that it is not a wasted effort. Now I must go; a shipment of some more gourmet cocoa awaits me. Good-bye and may we meet again soon!"
Vernon can teach MT moves from Generation IV onward that is listed for any particular pokémon. Check Bulbapedia to confirm eligibility for the move of interest.
There is a cap of 2 moves per visit. In order to revisit the Move Tutor, your character must change to another area and return after a minimum of two battles.
Here are some generic groupings for move costs. Moves will always fit into the more specific, and/or higher cost, category if they could potentially suit multiple brackets in the chart below; with the exception of moves that have no effect in single battles.
Eg: Roost It will cost x3 Heart Sweets because it heals HP even though it's single target.
Status Moves that: affect 1 target, buff/debuff a stat by 1, last under 5 turns, have no effect in single battles
Base Power 40 or less
Status Moves that: affect multiple targets and/or an area, buff/debuff a total of +2 for any stats, Heals HP
Base Power 70 or less
Status Moves that: flip stats, reflect/mimic damage, buff/debuff by 3+
Base Power 99 or Less
Base Power 100+
*This list will be updated over time and may have special exceptions added as things are brought to our attention