You can get that fragment instance either by 'ID' or by tag (you would need to give a tag while adding this fragment).
Now you can call any public method of that fragment using its instance.
For Example (Using tag), if you want to call a public method 'show()' of FragmentA. Then while adding it to the activity give it a tag like this:
Fragment fragmentA = new FragmentA();
getFragmentManager().beginTransaction()
.add(R.id.fragment_container,fragmentA,"YOUR_TARGET_FRAGMENT_TAG").commit();
And to get its instance (on a button click or as required):
FragmentA fragmentA = getFragmentManager().findFragmentByTag("YOUR_TARGET_FRAGMENT_TAG");
fragmentA.show();