After submitting your site to Google, you can use Google Site Search in your site. To do it, replace "mymobilesite" with the url of your site (without http://) in following code,
<input name="query" value="site:mymobilesite" type="hidden">
<input name="q" type="text" class="field">
<input value="Search" type="submit" class="button">
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License v3 as published by the Free Software Foundation.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses.