How to programmatically show next view in ViewPager?

Easiest way is:

nextButton.setOnClickListener { pager.arrowScroll(View.FOCUS_RIGHT) }
prevButton.setOnClickListener { pager.arrowScroll(View.FOCUS_LEFT) }

A complete implementation just for completeness:

public void MoveNext(View view) {
    //it doesn't matter if you're already in the last item
    pager.setCurrentItem(pager.getCurrentItem() + 1);
}

public void MovePrevious(View view) {
    //it doesn't matter if you're already in the first item
    pager.setCurrentItem(pager.getCurrentItem() - 1);
}

As blessenm answered viewpager.setCurrentItem(int index) is the way to go.