vou pegar como exemplo o p:calendar
Se utilizarmos o p:calendar, o código gerado, por exemplo, para
<h:form id="form1"><p:calendar id="val1"/></h:form>
é
<div id="form1:val1_inline" class="hasDatepicker"><div class="ui-datepicker-inline ui-datepicker ui-widget ui-widget-content ui-helper-clearfix ui-corner-all" style="display: block; "><div class="ui-datepicker-header ui-widget-header ui-helper-clearfix ui-corner-all"><a class="ui-datepicker-prev ui-corner-all" onclick="DP_jQuery_1319646491549.datepicker._adjustDate('#form1\\:val1_inline', -1, 'M');" title="Prev"><span class="ui-icon ui-icon-circle-triangle-w">Prev</span></a><a class="ui-datepicker-next ui-corner-all" onclick="DP_jQuery_1319646491549.datepicker._adjustDate('#form1\\:val1_inline', +1, 'M');" title="Next"><span class="ui-icon ui-icon-circle-triangle-e">Next</span></a><div class="ui-datepicker-title"><span class="ui-datepicker-month">October</span> <span class="ui-datepicker-year">2011</span></div></div><table class="ui-datepicker-calendar"><thead><tr><th class="ui-datepicker-week-end"><span title="Sunday">Su</span></th><th><span title="Monday">Mo</span></th><th><span title="Tuesday">Tu</span></th><th><span title="Wednesday">We</span></th><th><span title="Thursday">Th</span></th><th><span title="Friday">Fr</span></th><th class="ui-datepicker-week-end"><span title="Saturday">Sa</span></th></tr></thead><tbody><tr><td class=" ui-datepicker-week-end ui-datepicker-other-month ui-datepicker-unselectable ui-state-disabled"> </td><td class=" ui-datepicker-other-month ui-datepicker-unselectable ui-state-disabled"> </td><td class=" ui-datepicker-other-month ui-datepicker-unselectable ui-state-disabled"> </td><td class=" ui-datepicker-other-month ui-datepicker-unselectable ui-state-disabled"> </td><td class=" ui-datepicker-other-month ui-datepicker-unselectable ui-state-disabled"> </td><td class=" ui-datepicker-other-month ui-datepicker-unselectable ui-state-disabled"> </td><td class=" ui-datepicker-week-end " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">1</a></td></tr><tr><td class=" ui-datepicker-week-end " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">2</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">3</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">4</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">5</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">6</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">7</a></td><td class=" ui-datepicker-week-end " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">8</a></td></tr><tr><td class=" ui-datepicker-week-end " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">9</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">10</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">11</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">12</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">13</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">14</a></td><td class=" ui-datepicker-week-end " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">15</a></td></tr><tr><td class=" ui-datepicker-week-end " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">16</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">17</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">18</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">19</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">20</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">21</a></td><td class=" ui-datepicker-week-end " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">22</a></td></tr><tr><td class=" ui-datepicker-week-end " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">23</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">24</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">25</a></td><td class=" ui-datepicker-days-cell-over ui-datepicker-current-day ui-datepicker-today" onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default ui-state-highlight ui-state-active" href="#">26</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">27</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">28</a></td><td class=" ui-datepicker-week-end " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">29</a></td></tr><tr><td class=" ui-datepicker-week-end " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">30</a></td><td class=" " onclick="DP_jQuery_1319646491549.datepicker._selectDay('#form1\\:val1_inline',9,2011, this);return false;"><a class="ui-state-default" href="#">31</a></td><td class=" ui-datepicker-other-month ui-datepicker-unselectable ui-state-disabled"> </td><td class=" ui-datepicker-other-month ui-datepicker-unselectable ui-state-disabled"> </td><td class=" ui-datepicker-other-month ui-datepicker-unselectable ui-state-disabled"> </td><td class=" ui-datepicker-other-month ui-datepicker-unselectable ui-state-disabled"> </td><td class=" ui-datepicker-week-end ui-datepicker-other-month ui-datepicker-unselectable ui-state-disabled"> </td></tr></tbody></table></div></div>
Repare no id do objeto, ficou que várias tags pegaram id form1:val1****. Você pode pegar no jquery dessa forma.
Mas pelo que entendi, vc quer mudar as classes do css, o mais prático é fazer algo assim:
<h:form id="form1"><p:calendar id="val1" styleClass="classe1"/></h:form>
O componente que o prime para calendario usa é http://jqueryui.com/demos/datepicker/, com isso vc consegue buscar melhor o que você quer fazer.