From https://developers.facebook.com/docs/android/share

Facebook.java

private void publishStory() {
    Session session = Session.getActiveSession();

    if (session != null){

        // Check for publish permissions    
        List<String> permissions = session.getPermissions();
        if (!isSubsetOf(PERMISSIONS, permissions)) {
            pendingPublishReauthorization = true;
            Session.NewPermissionsRequest newPermissionsRequest = new Session
                    .NewPermissionsRequest(this, PERMISSIONS);
        session.requestNewPublishPermissions(newPermissionsRequest);
            return;
        }

        Bundle postParams = new Bundle();
        postParams.putString("name", "Facebook SDK for Android");
        postParams.putString("caption", "Build great social apps and get more installs.");
        postParams.putString("description", "The Facebook SDK for Android makes it easier and faster to develop Facebook integrated Android apps.");
        postParams.putString("link", "https://developers.facebook.com/android");
        postParams.putString("picture", "https://raw.github.com/fbsamples/ios-3.x-howtos/master/Images/iossdk_logo.png");

        Request.Callback callback= new Request.Callback() {
            public void onCompleted(Response response) {
                JSONObject graphResponse = response
                                           .getGraphObject()
                                           .getInnerJSONObject();
                String postId = null;
                try {
                    postId = graphResponse.getString("id");
                } catch (JSONException e) {
                    Log.i(TAG,
                        "JSON error "+ e.getMessage());
                }
                FacebookRequestError error = response.getError();
                if (error != null) {
                    Toast.makeText(getActivity()
                         .getApplicationContext(),
                         error.getErrorMessage(),
                         Toast.LENGTH_SHORT).show();
                    } else {
                        Toast.makeText(getActivity()
                             .getApplicationContext(), 
                             postId,
                             Toast.LENGTH_LONG).show();
                }
            }
        };

        Request request = new Request(session, "me/feed", postParams, 
                              HttpMethod.POST, callback);

        RequestAsyncTask task = new RequestAsyncTask(request);
        task.execute();
    }

}