Use application to rate it on market

public class AppRater {
private final static String APP_TITLE = "App Name";// App Name
private final static String APP_PNAME = "com.example.name";// Package Name

private final static int DAYS_UNTIL_PROMPT = 3;//Min number of days
private final static int LAUNCHES_UNTIL_PROMPT = 3;//Min number of launches

public static void app_launched(Context mContext) {
    SharedPreferences prefs = mContext.getSharedPreferences("apprater", 0);
    if (prefs.getBoolean("dontshowagain", false)) { return ; }

    SharedPreferences.Editor editor = prefs.edit();

    // Increment launch counter
    long launch_count = prefs.getLong("launch_count", 0) + 1;
    editor.putLong("launch_count", launch_count);

    // Get date of first launch
    Long date_firstLaunch = prefs.getLong("date_firstlaunch", 0);
    if (date_firstLaunch == 0) {
        date_firstLaunch = System.currentTimeMillis();
        editor.putLong("date_firstlaunch", date_firstLaunch);
    }

    // Wait at least n days before opening
    if (launch_count >= LAUNCHES_UNTIL_PROMPT) {
        if (System.currentTimeMillis() >= date_firstLaunch + 
                (DAYS_UNTIL_PROMPT * 24 * 60 * 60 * 1000)) {
            showRateDialog(mContext, editor);
        }
    }

    editor.commit();
}   

public static void showRateDialog(final Context mContext, final SharedPreferences.Editor editor) {
    final Dialog dialog = new Dialog(mContext);
    dialog.setTitle("Rate " + APP_TITLE);

    LinearLayout ll = new LinearLayout(mContext);
    ll.setOrientation(LinearLayout.VERTICAL);

    TextView tv = new TextView(mContext);
    tv.setText("If you enjoy using " + APP_TITLE + ", please take a moment to rate it. Thanks for your support!");
    tv.setWidth(240);
    tv.setPadding(4, 0, 4, 10);
    ll.addView(tv);

    Button b1 = new Button(mContext);
    b1.setText("Rate " + APP_TITLE);
    b1.setOnClickListener(new OnClickListener() {
        public void onClick(View v) {
            mContext.startActivity(new Intent(Intent.ACTION_VIEW, Uri.parse("market://details?id=" + APP_PNAME)));
            dialog.dismiss();
        }
    });        
    ll.addView(b1);

    Button b2 = new Button(mContext);
    b2.setText("Remind me later");
    b2.setOnClickListener(new OnClickListener() {
        public void onClick(View v) {
            dialog.dismiss();
        }
    });
    ll.addView(b2);

    Button b3 = new Button(mContext);
    b3.setText("No, thanks");
    b3.setOnClickListener(new OnClickListener() {
        public void onClick(View v) {
            if (editor != null) {
                editor.putBoolean("dontshowagain", true);
                editor.commit();
            }
            dialog.dismiss();
        }
    });
    ll.addView(b3);

    dialog.setContentView(ll);        
    dialog.show();        
}}

Now Integrate class to your activity like this ->

AppRater.app_launched(this);

I always use a method like this one:

private void launchMarket() {
    Uri uri = Uri.parse("market://details?id=" + getPackageName());
    Intent goToMarket = new Intent(Intent.ACTION_VIEW, uri);
    try {
        startActivity(goToMarket);
    } catch (ActivityNotFoundException e) {
        Toast.makeText(this, R.string.couldnt_launch_market, Toast.LENGTH_LONG).show();
    }
}