This example demonstates what OpenLayers provides for map navigation on mobile.
The TouchNavigation control allows to pan the map with touch gestures on the screen – "touchstart", "touchmove", "touchend" sequences. It also allows to zoom in with double taps, and to zoom out with two-finger single taps. The latter is only available on devices supporting multi-touch. Note that in most devices Android doesn't support multi-touch in the browser.
The ZoomPanel control provides + and - buttons for zooming in and out. These buttons should work on any device, and the zoom out button is especially needed for devices that don't support multi-touch.
See the mobile-navigation.js source to see how this is done.