Using Async task

call when you want to download file : new DownloadFileFromURL().execute(file_url);

public class MainActivity extends Activity {

    // Progress Dialog
    private ProgressDialog pDialog;
    public static final int progress_bar_type = 0;

    // File url to download
    private static String file_url = "http://www.qwikisoft.com/demo/ashade/20001.kml";

    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);

        setContentView(R.layout.activity_main);

        new DownloadFileFromURL().execute(file_url);

    }

    /**
     * Showing Dialog
     * */

    @Override
    protected Dialog onCreateDialog(int id) {
        switch (id) {
        case progress_bar_type: // we set this to 0
            pDialog = new ProgressDialog(this);
            pDialog.setMessage("Downloading file. Please wait...");
            pDialog.setIndeterminate(false);
            pDialog.setMax(100);
            pDialog.setProgressStyle(ProgressDialog.STYLE_HORIZONTAL);
            pDialog.setCancelable(true);
            pDialog.show();
            return pDialog;
        default:
            return null;
        }
    }

    /**
     * Background Async Task to download file
     * */
    class DownloadFileFromURL extends AsyncTask<String, String, String> {

        /**
         * Before starting background thread Show Progress Bar Dialog
         * */
        @Override
        protected void onPreExecute() {
            super.onPreExecute();
            showDialog(progress_bar_type);
        }

        /**
         * Downloading file in background thread
         * */
        @Override
        protected String doInBackground(String... f_url) {
            int count;
            try {
                URL url = new URL(f_url[0]);
                URLConnection connection = url.openConnection();
                connection.connect();

                // this will be useful so that you can show a tipical 0-100%
                // progress bar
                int lenghtOfFile = connection.getContentLength();

                // download the file
                InputStream input = new BufferedInputStream(url.openStream(),
                        8192);

                // Output stream
                OutputStream output = new FileOutputStream(Environment
                        .getExternalStorageDirectory().toString()
                        + "/2011.kml");

                byte data[] = new byte[1024];

                long total = 0;

                while ((count = input.read(data)) != -1) {
                    total += count;
                    // publishing the progress....
                    // After this onProgressUpdate will be called
                    publishProgress("" + (int) ((total * 100) / lenghtOfFile));

                    // writing data to file
                    output.write(data, 0, count);
                }

                // flushing output
                output.flush();

                // closing streams
                output.close();
                input.close();

            } catch (Exception e) {
                Log.e("Error: ", e.getMessage());
            }

            return null;
        }

        /**
         * Updating progress bar
         * */
        protected void onProgressUpdate(String... progress) {
            // setting progress percentage
            pDialog.setProgress(Integer.parseInt(progress[0]));
        }

        /**
         * After completing background task Dismiss the progress dialog
         * **/
        @Override
        protected void onPostExecute(String file_url) {
            // dismiss the dialog after the file was downloaded
            dismissDialog(progress_bar_type);

        }

    }
}

if not working in 4.0 then add:

StrictMode.ThreadPolicy policy = new StrictMode.ThreadPolicy.Builder().permitAll().build();
StrictMode.setThreadPolicy(policy); 

How to download file from Url

fun downloadPdf(baseActivity:Context,url: String?,title: String?): Long {
        val direct = File(Environment.getExternalStorageDirectory().toString() + "/your_folder")

        if (!direct.exists()) {
            direct.mkdirs()
        }
        val extension = url?.substring(url.lastIndexOf("."))
        val downloadReference: Long
         var  dm: DownloadManager
         dm= baseActivity.getSystemService(Context.DOWNLOAD_SERVICE) as DownloadManager
        val uri = Uri.parse(url)
        val request = DownloadManager.Request(uri)
        request.setDestinationInExternalPublicDir(
                "/your_folder",
                "pdf" + System.currentTimeMillis() + extension
        )
        request.setNotificationVisibility(DownloadManager.Request.VISIBILITY_VISIBLE_NOTIFY_COMPLETED)
        request.setTitle(title)
        Toast.makeText(baseActivity, "start Downloading..", Toast.LENGTH_SHORT).show()

        downloadReference = dm?.enqueue(request) ?: 0

        return downloadReference

    }

Bofore calling this method do check for Runtime permission:

Manifest.permission.WRITE_EXTERNAL_STORAGE

Nowadays the built-in Android browser has been replaced by Chrome, which does this perfectly well. You can long-press and save virtually any image or link, and even videos from a number of sites that couldn't be easily done on the desktop.

Answer below for older devices:

The Android browser by default can only download files that the Android system "recognizes" (i.e., there has to be a program registered to handle that file type). It's a stupid restriction in my opinion, but you can install Download Crutch to overcome this limitation (it registers itself for every filetype).

If you're referring to images that link to something else and you want to save the something else, long-press on the image and choose "Save Link As" or similar.

try this

public class MyAsnyc extends AsyncTask<Void, Void, Void> {
    public static File file;
    InputStream is;

    protected void doInBackground() throws IOException {

        File path = Environment.getExternalStoragePublicDirectory(Environment.DIRECTORY_PICTURES);
        file = new File(path, "DemoPicture.jpg");
        try {    
            // Make sure the Pictures directory exists.
            path.mkdirs();

            URL url = new URL("http://androidsaveitem.appspot.com/downloadjpg");
            /* Open a connection to that URL. */
            URLConnection ucon = url.openConnection();

            /*
             * Define InputStreams to read from the URLConnection.
             */
            is = ucon.getInputStream();

            OutputStream os = new FileOutputStream(file);
            byte[] data = new byte[is.available()];
            is.read(data);
            os.write(data);
            is.close();
            os.close();

        } catch (IOException e) {
            Log.d("ImageManager", "Error: " + e);
        }
    }

    @Override
    protected Void doInBackground(Void... params) {
        // TODO Auto-generated method stub
        try {
            doInBackground();
        } catch (IOException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }

        return null;
    }

    protected void onPostExecute() {
        try {
            // Tell the media scanner about the new file so that it is
            // immediately available to the user.
            MediaScannerConnection.scanFile(null,
                    new String[]{file.toString()}, null,
                    new MediaScannerConnection.OnScanCompletedListener() {
                        public void onScanCompleted(String path, Uri uri) {
                            Log.i("ExternalStorage", "Scanned " + path + ":");
                            Log.i("ExternalStorage", "-> uri=" + uri);
                        }
                    });
        } catch (IOException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }

    }
}