Finalmente logré mostrar el mapa. Ahora, quiero mostrar mi ubicación actual, intenté usar este código pero no funcionó cuando hice clic en el botón de mi ubicación en la esquina superior derecha.

AndroidManifest.xml

<uses-permission android:name="android.permission.ACCESS_FINE_LOCATION" />
<uses-permission android:name="android.permission.INTERNET"/>
<uses-permission android:name="android.permission.ACCESS_NETWORK_STATE"/>
<uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE"/>
<uses-permission android:name="android.permission.ACCESS_COARSE_LOCATION"/>
<uses-permission android:name="com.example.hp.testmap.MAPS_RECEIVE"></uses-permission>
<uses-permission android:name="com.google.android.providers.gsf.permission.READ_GSERVICES" />

<permission
    android:name="com.example.hp.testmap.permission.MAPS_RECEIVE"
    android:protectionLevel="signature"/>

    <uses-feature
        android:glEsVersion="0x00020000"
        android:required="true"/>

MapsActivity.java

public void onMapReady(GoogleMap googleMap) {
    mMap = googleMap;
    mMap.setMyLocationEnabled(true);
   if (ActivityCompat.checkSelfPermission(this, Manifest.permission.ACCESS_FINE_LOCATION) != PackageManager.PERMISSION_GRANTED && ActivityCompat.checkSelfPermission(this, Manifest.permission.ACCESS_COARSE_LOCATION) != PackageManager.PERMISSION_GRANTED) {

       LocationManager locationManager = (LocationManager) getSystemService(Context.LOCATION_SERVICE);

       Criteria criteria = new Criteria();

       String provider = locationManager.getBestProvider(criteria, true);

       Location myLocation = locationManager.getLastKnownLocation(provider);

       mMap.setMapType(GoogleMap.MAP_TYPE_NORMAL);

        double latitude = myLocation.getLatitude();

        double longitude = myLocation.getLongitude();

        LatLng latLng = new LatLng(latitude, longitude);

        mMap.moveCamera(CameraUpdateFactory.newLatLng(latLng));

        mMap.animateCamera(CameraUpdateFactory.zoomTo(20));
        return;
    }

}