Below is a listing of iOS finger gestures arranged by gesture type. All text, single document. Verified in iOS 10, using VoiceOver Practice; (Settings>General>Accessibility>VoiceOver>VoiceOver Practice).
Additional tips given at bottom.
Note: Much of the information gathered below is a rearrangement of Apple's original materials. Some editing has been performed to better fit the layout. Some editor's additions have been included, from experience and use.
Portions copyright Apple, Inc. All rights reserved.
The most direct method of navigation is to lightly drag a finger around on the screen and listen to what it touches. VoiceOver will speak everything you touch.
Use thumb and forefinger, like turning a knob on the surface, to choose different Rotor settings and navigation modes. The Rotor can be turned in both directions. Use 1 Finger flick up and down, to adjust each setting or to navigate in the chosen mode.
You can also place a finger from one hand on the screen, then drag a finger from the other hand around it in a circular motion and it will turn the Rotor.
Flick Right or Left
1 Finger: move focus to next or previous item.
2 Fingers: not mapped.
3 Fingers: scroll left or right one page.
4 Fingers: switch to next or previous running app.
Flick Up or Down
1 Finger Up/Down: move focus to next or previous item using Rotor setting. Or change the status of the current Rotor setting.
2 Fingers Down:, read page starting at selected item.
2 Fingers Up: read page starting at top.
3 Fingers Up/Down: scroll up or down one page.
3 Fingers Down when VoiceOver Focus is in the Status Bar: loads Notification Center.
3 Fingers Up when VoiceOver Focus is in the Status Bar: loads Control Center.
4 Fingers: not mapped.
1 Finger: select an item without activating.
2 Fingers: if VoiceOver is speaking, pauses and resumes speaking.
3 Fingers: speak page numbers or rows being displayed.
4 Fingers Near Top: move to first element on the screen (usually top-left corner element).
4 Fingers Near Bottom: move to last element on the screen (usually bottom-right corner element).
1 Finger: activate the selected item.
2 Fingers: stop and start the current activity. Answers or hangs up a call, pauses or resumes a video or music, plus others. See VoiceOver practice.
3 Fingers: toggles speech on and off.
4 Fingers: toggles VoiceOver help on or off.
1 Finger: double tap the selected item.
2 Fingers: activate Item Chooser.
3 Fingers: toggles Screen Curtain on and off.
4 Fingers: not mapped.
Unique Gestures and Tips
Quadruple Tap with 3 Fingers: copy last spoken phrase to the clipboard.
Double Tap with 1 Finger and Hold: drags the selected item. On the Home screen, move, edit or delete apps. In text, pop-up window with editing options.
Double Tap with 2 Fingers and Hold: set a custom label.
Split Tap: place a finger on the selected item, then tap anywhere with another finger to activate the selection.
Activate Anywhere: when a item is selected, you can double-tap anywhere on the screen to activate the item. No need to tap directly on the item.
2 Finger Scrub: like drawing a 'Z' with both fingers close together. Dismisses alerts or goes back one screen.
2 Finger Double Tap: when editing text in any field or app, starts and stops dictation.
One Finger Double Tap and Drag: adjust a slider to a new position.
Triple Click Home Button: turns VoiceOver on and off (cam be customized in Settings>General>Accessibility>Accessibility Shortcut).
App Switcher: double-click the Home button to access all running apps; 1 finger flick left or right to move between the apps; double-tap an app with 1 finger to switch to that app; 3 finger flick up to quit a running app.
2 Finger Pinch Open: select text.
2 Finger Pinch Close: unselect text..
4 Finger Tap Near Right Side of Screen: move focus to next app.
4 Finger Tap Near Left Side of Screen: move focus to previous app.
Note: it is entirely possible that I have overlooked a gesture, so please let me know in the comments of any others that you are aware of.