How do I switch chambers smoothly on a multichamber ocarina?

While the action of switching chambers appears to be simply sliding the ocarina from side to side, there is more to it.

When playing, the ocarina is pressed lightly against the lips, if this pressure is maintained while switching the mouthpiece will grip against the lips, creating friction that switching harder.

Chamber switching is easier if this pressure is released. So the process to switch chambers is as follows:

  1. Slightly move the ocarina away from the lips, such that the mouthpiece is not touching them. This distance should be minimal, only what is required to break contact.
  2. Move to the desired windway.
  3. Move the mouthpiece back into contact with the lips.

If you practice doing this, after a few days it becomes automatic. Note that you don't actually have to break contact, just reduce the pressure against the skin and consequently friction. Lightly tonguing the switch also helps.

It is easiest to when the ocarina's mouthpiece is ergonomically designed. The edge should be as thin as possible and somewhat rounded.

An ocarina mouthpiece with good ergonomic design should have a rounded edge to match the curvature of the lips, instead of digging into them
Ocarina mouthpieces with a square edge are bad for ergonomics as the human lips are curved, and a square edge will dig into them for no reason

Special notes for plain-finish ocarinas

The rougher surface of plain clay slides over skin far more easily than a smooth surface, though it can still cling if moisture is present.

This can be addressed by touching your lips to the ocarina's mouthpiece for some time before playing; the porous clay will absorb any moisture present. Always keep your head and the ocarina up, as looking down can allow saliva to run onto the lips/mouthpiece.