Right now I have a ViewPager with two different Fragments, and I currently indicate to swipe left and right with two chevrons. However, someone might mistake those icons for buttons, and I would like something that indicates a swipe in an intuitive way that doesn't look like a button that they can click on.
I've encountered a similar problem and solved it by simply adding animation to reveal the "hidden" bits.
If the user taps somewhere on the element, you can add a bounce effect which momentarily reveals the next/previous pages. From my own user testing this is a very intuitive way to show the users they can swipe.
Example: GIF of demo.
If your users are using the chevrons like buttons, then why not make them work like buttons? The other answers here give some good cues for swipe-ability, but it seems that having buttons that do the same thing is a good bit of redundancy.
A few options come to mind:
Adding a page indicator: a row of dots/bullets/circles with the active one different from the rest. This should alert the user to the existence of other pages than can be reached by swiping.
“Shaking” the page a bit when it first appears, showing part of the other pages.
Add an overlay with explicative text and/or graphic, probably only the first time.
A combination of the above.
Usually when we use swipable content we have dots at the bottom which indicate the number of swipable content, as Rob has mentioned.
We also sometimes fade the content on the right or left. You can see an example when selecting sizes and colors on banana Republic or gap mobile websites.