I have been following the Android Development course on Udacity, and got to a lesson where we were to implement a ShareActionProvider. After attempting it myself, and then following what they did--I'm certain it's not working properly.
I'm putting the code in a Fragment; the correct item is present in the overflow menu, but when I click "Share", nothing happens. I noticed when I open the DetailsActivity, that the following appears in the logs:
17493-17493/com.dummy.sunshine.app W/MenuItemCompat﹕ setActionProvider: item does not implement SupportMenuItem; ignoring
I'm not sure what that means, but I couldn't find anything about it online. I would assume that clicking it is supposed to do something--however, they never go over what's supposed to happen after that lesson--so I'm a tad confused.
DetailActivity.java
import android.content.Intent;
import android.os.Bundle;
import android.support.v4.app.FragmentActivity;
import android.view.Menu;
import android.view.MenuItem;
public class DetailActivity extends FragmentActivity {
    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_detail);
    }
    @Override
    public boolean onCreateOptionsMenu(Menu menu) {
        // Inflate the menu; this adds items to the action bar if it is present.
        getMenuInflater().inflate(R.menu.menu_detail, menu);
        return true;
    }
    @Override
    public boolean onOptionsItemSelected(MenuItem item) {
        // Handle action bar item clicks here. The action bar will
        // automatically handle clicks on the Home/Up button, so long
        // as you specify a parent activity in AndroidManifest.xml.
        int id = item.getItemId();
        switch (id) {
            case R.id.action_settings:
                startActivity(new Intent(this, SettingsActivity.class));
                return true;
        }
        return super.onOptionsItemSelected(item);
    }
}
DetailFragment.java
import android.content.Intent;
import android.os.Bundle;
import android.support.v4.app.Fragment;
import android.support.v4.view.MenuItemCompat;
import android.support.v7.widget.ShareActionProvider;
import android.util.Log;
import android.view.LayoutInflater;
import android.view.Menu;
import android.view.MenuInflater;
import android.view.MenuItem;
import android.view.View;
import android.view.ViewGroup;
import android.widget.TextView;
/**
 * A placeholder fragment containing a simple view.
 */
public class DetailFragment extends Fragment {
    private static String mForecastStr;
    private final String TAG = DetailActivity.class.getSimpleName();
    public DetailFragment() {
        setHasOptionsMenu(true);
    }
    @Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container,
                             Bundle savedInstanceState) {
        View rootView = inflater.inflate(R.layout.fragment_detail, container, false);
        Intent intent = getActivity().getIntent(); //allows us to get data from the screen that sent us to this activity
        if (intent != null && intent.hasExtra(Intent.EXTRA_TEXT)) {
            mForecastStr = intent.getStringExtra(Intent.EXTRA_TEXT); //we get the EXTRA_TEXT that the ForecastFragment sent us
            ((TextView) rootView.findViewById(R.id.detail_text))
                    .setText(mForecastStr);
        }
        return rootView;
    }
    private Intent shareDetailForecast() {
        Intent sendIntent = new Intent();
        sendIntent.setAction(Intent.ACTION_SEND);
        sendIntent.setType("text/plain");
        sendIntent.putExtra(Intent.EXTRA_TEXT, mForecastStr + "#SunshineApp");
        return sendIntent;
    }
    @Override
    public void onCreateOptionsMenu(Menu menu, MenuInflater inflater) {
        // Inflate the menu; this adds items to the action bar if it is present.
        inflater.inflate(R.menu.menu_detail_fragment, menu);
        MenuItem menuItem = menu.findItem(R.id.action_share);
        ShareActionProvider mShareActionProvider = new ShareActionProvider(getActivity());
        mShareActionProvider.setShareIntent(shareDetailForecast());
        MenuItemCompat.setActionProvider(menuItem, mShareActionProvider);
        if (mShareActionProvider != null) {
            mShareActionProvider.setShareIntent(shareDetailForecast());
        } else {
            Log.d(TAG, "mShareActionProvider is null...");
        }
    }
}
menu_detail_fragment.xml
<?xml version="1.0" encoding="utf-8"?>
<menu xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto">
    <item android:id="@+id/action_share"
        android:title="@string/action_share"
        android:orderInCategory="5"
        app:showAsAction="ifRoom"
        app:actionProviderClass="android.support.v7.widget.ShareActionProvider" />
</menu>
menu_detail.xml
<menu xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    xmlns:tools="http://schemas.android.com/tools"
    tools:context="com.nxt3.sunshine.app.DetailActivity">
    <item android:id="@+id/action_settings"
        android:title="@string/action_settings"
        android:orderInCategory="100"
        app:showAsAction="never" />
</menu>
This is what the app looks like on the DetailActivity page:

                        
I believe your problem is that on your DetailActivity you are extending a FragmentActivity while you should be extending an AppCompatActivity (which is a subclass of the FragmentActivity), as you are using an action bar on your activity and using the support library.
so you should replace this:
by this:
and import the support library:
I don't know if you already have it set, but you also need to set your AppTheme to be Theme.AppCompat or something similar on your AndroidManifest.xml. Something like below:
I'm doing the same exercise in the Udacity and that worked for me, I hope it helps.