Where, how and when I can acquire HM's?

X/Y HM Locations

Cut - Parfum Palace - In the maze in the garden at the back of the palace

Fly - Courmaline City - From Professor Sycamore in a cut scene - can be used outside of battle after defeating Ramos in Coumarine City Gym and earning the Plant badge

Surf - Shalour City - From Calem/Serena, after defeating Korrina at the top of the Tower of Mastery - can be used already by the time you obtain it, after beating Shalour City Gym

Strength - Cyllage City - From Grant

Waterfall - Route 19 - From Shauna

Also useful to note - Rock Smash is no longer a HM but you can get it in Ambrette town, from a girl outside the Pokemon centre.

The same goes for Flash which is now a "nice-to-have" tool for lowering the amount of fights in caves. You can get it from your Dancing friend in Glittering cave.

TM and HM list will show you every TM and HM you can get, and how to do so.

You do get the Fly HM in Courmaline City from the professor..