Most probably you won’t need to customize $this->getUrl(’’) method as it’s general method of creating router specific URLs.
Basic format is <?=$this->getUrl('module/controller/action', array('param'=>$value))?>
getLogoSrc, getLogoAlt are methods of the block class that is rendering this template.
You can find the class name from the layout tag that is refering to this template.
Your example is coming form template/page/html/header.phtml which is refered from layout/core/default.xml.
The block definition there is < block type="page/html_header" name="header" as="header" >
Which means that the class called is Mage_Page_Block_Html_Header.
There you can find the methods