I suppose the first point to make is that you shouldn't depend on invisible interactions to accomplish anything.
The example made in virtualnobi's comment of iOS's swipe-to-delete gesture is a good example; Mail items etc. can be deleted the long way by choosing Edit, then checking the items you wish to delete, then choosing "Trash"/"Archive" at the bottom of the screen, or they can be deleted by swiping the item to the side until the "Trash"/"Archive" state is visible. In this way, the swipe gesture is a useful pro tip, but never a requirement for normal users.
When a swipe action is required by the interface (e.g. to prevent accidental activation), the behaviour should be simply indicated. Animation is a great choice for this. For example, the little shine effect over the "slide to unlock" text on iOS provides a useful hint of the kind of motion required (horizontal slide):
Image taken from this Stack Overflow question
Where such an obnoxious animation is not feasible, putting an icon on the screen that indicates that there is an alternative interaction can provide a useful cue. Again, iOS has an example with the camera button on the lock screen—tapping it once can't launch the camera immediately since that would be constantly activated by accident, but expecting users to know that grabbing the icon and swiping up is how to activate the camera is another invisible interaction. So Apple adds a tiny indication of the affordance of that button when tapped once; quickly bouncing the lock screen vertically and briefly showing the camera interface beneath it. The user learns quickly that swiping up a little further reveals a little more of the camera interface, until swiping up in one go unlocks the interface and prevents the lock screen coming back down:
Animation taken from UI Animations tumblr
This is very similar to the lock screen affordance on Windows Phone, as mentioned in this highly relevant article about animations as affordance:
Animation is a great way to provide affordance of content overflowing. In Windows Phone, the transition animations tilt the content being viewed about the y axis so that (for a split second) more than a screenful of content is visible. This is a helpful indication that there's more off to the side of the screen than what is immediately visible. This is a huge pain to find a good example of online (this is the best I can find and it's a real blink-and-you-miss-it example), but it's very apparent when using the device in person. In Windows Phone they also show a tiny sliver of the content on the next screen across horizontally (as a hint that there's more than meets the eye).
This technique (especially the animation example) is an example of what Edward C. Tolman calls "latent learning" (learning through passive observation rather than being told explicitly). There's a good article on the Microsoft website that gives another example:
In the following image, the list box’s contents slide in when the
control is initiated, which conveys a lot of information quickly. This
transition suggests that users can scroll through this list and that
it contains more content beyond the current display, which helps
encourage user interaction.
If the list box appears empty for just a moment, and then its content
slides in, the user sees this movement and can infer that the list box
contains more options than what currently appears. Likewise, the
sliding movement acts as a clue that users can manipulate the content
that appears.
