From Josh Holtz's example on GitHub:

You should add MapView in your Layout like

 <com.google.android.gms.maps.MapView 
    android:id="@+id/mapview"
    android:layout_width="fill_parent" 
    android:layout_height="fill_parent" />

and implement your Fragment like

public class SomeFragment extends Fragment {

MapView mapView;
GoogleMap map;

@Override
public View onCreateView(LayoutInflater inflater, ViewGroup container, Bundle savedInstanceState)          {
    View v = inflater.inflate(R.layout.some_layout, container, false);

    // Gets the MapView from the XML layout and creates it
    mapView = (MapView) v.findViewById(R.id.mapview);
    mapView.onCreate(savedInstanceState);

    // Gets to GoogleMap from the MapView and does initialization stuff
    map = mapView.getMap();
    map.getUiSettings().setMyLocationButtonEnabled(false);
    map.setMyLocationEnabled(true);

    // Needs to call MapsInitializer before doing any CameraUpdateFactory calls
    try {
        MapsInitializer.initialize(this.getActivity());
    } catch (GooglePlayServicesNotAvailableException e) {
        e.printStackTrace();
    }

    // Updates the location and zoom of the MapView
    CameraUpdate cameraUpdate = CameraUpdateFactory.newLatLngZoom(new LatLng(43.1, -87.9), 10);
    map.animateCamera(cameraUpdate);

    return v;
}

@Override
public void onResume() {
    mapView.onResume();
    super.onResume();
}

@Override
public void onDestroy() {
    super.onDestroy();
    mapView.onDestroy();
 }

 @Override
 public void onLowMemory() {
    super.onLowMemory();
    mapView.onLowMemory();
  }

}

Adding to M D's answer:

From documentation:

A GoogleMap must be acquired using getMapAsync(OnMapReadyCallback). The MapView automatically initializes the maps system and the view.

According to this, the more correct way to initialize GoogleMap is using getMapAsync.

Note that your class has to implement OnMapReadyCallback

@Override
public View onCreateView(LayoutInflater inflater, ViewGroup container,
                         Bundle savedInstanceState) {
    View v = inflater.inflate(R.layout.fragment_map_page, container, false);

    mMapView = (MapView) v.findViewById(R.id.map_view);
    mMapView.onCreate(savedInstanceState);
    mMapView.getMapAsync(this); //this is important

    return v;
}

@Override
public void onMapReady(GoogleMap googleMap) {
    mGoogleMap = googleMap;
    mGoogleMap.getUiSettings().setZoomControlsEnabled(true);
    mGoogleMap.addMarker(new MarkerOptions().position(/*some location*/));
    mGoogleMap.moveCamera(CameraUpdateFactory.newLatLngZoom(/*some location*/, 10));
}

@Override
public void onResume() {
    super.onResume();
    mMapView.onResume();
}

@Override
public void onPause() {
    super.onPause();
    mMapView.onPause();
}

@Override
public void onDestroy() {
    super.onDestroy();
    mMapView.onDestroy();
}

@Override
public void onSaveInstanceState(Bundle outState) {
    super.onSaveInstanceState(outState);
    mMapView.onSaveInstanceState(outState);
}

@Override
public void onLowMemory() {
    super.onLowMemory();
    mMapView.onLowMemory();
}

In case somebody is looking for a Kotlin version of MapView Fragment ;)

class MapViewKotlinFragment : Fragment(), OnMapReadyCallback {

private var mMap: MapView? = null

override fun onSaveInstanceState(outState: Bundle?) {
    super.onSaveInstanceState(outState)

    mMap?.onSaveInstanceState(outState)
}

override fun onCreateView(inflater: LayoutInflater?, container: ViewGroup?, savedInstanceState: Bundle?): View? {
    val view = inflater?.inflate(R.layout.fragment_map, container, false)

    mMap = view?.findViewById(R.id.mapViewPlaces) as MapView
    mMap?.onCreate(savedInstanceState)
    mMap?.getMapAsync(this)

    return view
}

override fun onResume() {
    super.onResume()
    mMap?.onResume()
}

override fun onPause() {
    super.onPause()
    mMap?.onPause()
}

override fun onStart() {
    super.onStart()
    mMap?.onStart()
}

override fun onStop() {
    super.onStop()
    mMap?.onStop()
}

override fun onDestroy() {
    super.onDestroy()
    mMap?.onDestroy()
}

override fun onLowMemory() {
    super.onLowMemory()
    mMap?.onLowMemory()
}

override fun onMapReady(googleMap: GoogleMap) {
    googleMap.addMarker(MarkerOptions().position(LatLng(0.0, 0.0)).title("Marker"))
}