Ejemplo 01 - AsyncTask

activity_main.xml

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:paddingBottom="@dimen/activity_vertical_margin"
    android:paddingLeft="@dimen/activity_horizontal_margin"
    android:paddingRight="@dimen/activity_horizontal_margin"
    android:paddingTop="@dimen/activity_vertical_margin"
    tools:context="org.josejuansanchez.ejemploasynctask.MainActivity"
    android:orientation="vertical">

    <Button
        android:id="@+id/button"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:text="Load image"
        android:layout_weight="1" />

    <ImageView
        android:id="@+id/imageview"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_gravity="center"
        android:gravity="center"
        android:layout_weight="2" />


</LinearLayout>

AndroidManifest.xml

Recuerda incluir este permiso

<uses-permission android:name="android.permission.INTERNET" />

ImageBackgroundTask.java

public class ImageBackgroundTask extends AsyncTask<String, Void, Bitmap> {

    Activity mActivity;

    public ImageBackgroundTask(Activity activity) {
        mActivity = activity;
    }

    @Override
    protected Bitmap doInBackground(String... params) {
        return downloadImage(params[0]);
    }

    private Bitmap downloadImage(String urlString) {
        URL url;
        try {
            url = new URL(urlString);
            HttpURLConnection httpCon = (HttpURLConnection) url.openConnection();

            InputStream is = httpCon.getInputStream();
            int fileLength = httpCon.getContentLength();

            ByteArrayOutputStream buffer = new ByteArrayOutputStream();
            int nRead, totalBytesRead = 0;
            byte[] data = new byte[2048];

            while ((nRead = is.read(data, 0, data.length)) != -1) {
                buffer.write(data, 0, nRead);
                totalBytesRead += nRead;
            }

            byte[] image = buffer.toByteArray();
            Bitmap bitmap = BitmapFactory.decodeByteArray(image, 0, image.length);
            return bitmap;
        } catch (Exception e) {
            e.printStackTrace();
        }
        return null;
    }

    @Override
    protected void onPostExecute(Bitmap result) {
        Log.i("ImageBackgroundTask", "onPostExecute Called");

        if (result != null) {
            ((ImageView) mActivity.findViewById(R.id.imageview)).setImageBitmap(result);
        }

    }
}

MainActivity.java

public class MainActivity extends AppCompatActivity implements View.OnClickListener {

    Button mButton;
    TextView mTextView;
    String mUrl[] = {
            "https://upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Android_robot.svg/511px-Android_robot.svg.png",
            "http://innatia.info/images/galeria/coco-0.jpg",
            "http://cuantas-calorias.org/wp-content/uploads/2015/01/calorias-de-la-naranja.jpg"
    };

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        mButton = (Button) findViewById(R.id.button);
        mTextView = (TextView) findViewById(R.id.textview);

        mButton.setOnClickListener(this);
    }

    @Override
    public void onClick(View v) {
        Random ran = new Random();
        int index = ran.nextInt(3);

        new ImageBackgroundTask(this).execute(mUrl[index]);
    }

    public void setText(String newText) {
        mTextView.setText(newText);
    }
}