This is the methods I use to copy a file to the sd card when the app is first installed:
public class StartUp extends Activity {
    /**
     * -- Called when the activity is first created.
     * ==============================================================
     **/
    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        FirstRun();
    }
    private void FirstRun() {
        SharedPreferences settings = this.getSharedPreferences("YourAppName", 0);
        boolean firstrun = settings.getBoolean("firstrun", true);
        if (firstrun) { // Checks to see if we've ran the application b4
            SharedPreferences.Editor e = settings.edit();
            e.putBoolean("firstrun", false);
            e.commit();
            // If not, run these methods:
            SetDirectory();
            Intent home = new Intent(StartUp.this, MainActivity.class);
            startActivity(home);
        } else { // Otherwise start the application here:
            Intent home = new Intent(StartUp.this, MainActivity.class);
            startActivity(home);
        }
    }
/**
     * -- Check to see if the sdCard is mounted and create a directory w/in it
     * ========================================================================
     **/
    private void SetDirectory() {
        if (android.os.Environment.getExternalStorageState().equals(android.os.Environment.MEDIA_MOUNTED)) {
            extStorageDirectory = Environment.getExternalStorageDirectory().toString();
            File txtDirectory = new File(extStorageDirectory + "/yourAppName/txt/");
            // Create
            // a
            // File
            // object
            // for
            // the
            // parent
            // directory
            txtDirectory.mkdirs();// Have the object build the directory
            // structure, if needed.
            CopyAssets(); // Then run the method to copy the file.
        } else if (android.os.Environment.getExternalStorageState().equals(android.os.Environment.MEDIA_MOUNTED_READ_ONLY)) {
            AlertsAndDialogs.sdCardMissing(this);//Or use your own method ie: Toast
        }
    }
    /**
     * -- Copy the file from the assets folder to the sdCard
     * ===========================================================
     **/
    private void CopyAssets() {
        AssetManager assetManager = getAssets();
        String[] files = null;
        try {
            files = assetManager.list("");
        } catch (IOException e) {
            Log.e("tag", e.getMessage());
        }
        for (int i = 0; i < files.length; i++) {
            InputStream in = null;
            OutputStream out = null;
            try {
                in = assetManager.open(files[i]);
                out = new FileOutputStream(extStorageDirectory + "/yourAppName/txt/" + files[i]);
                copyFile(in, out);
                in.close();
                in = null;
                out.flush();
                out.close();
                out = null;
            } catch (Exception e) {
                Log.e("tag", e.getMessage());
            }
        }
    }
    private void copyFile(InputStream in, OutputStream out) throws IOException {
        byte[] buffer = new byte[1024];
        int read;
        while ((read = in.read(buffer)) != -1) {
            out.write(buffer, 0, read);
        }
    }