You can just use the HTML autofocus attribute.
<div id = "inputBox">
<form action = "something" method = "post">
<label for = "searcher">Click here to get into the box
<input id = "searcher" type = "text" name = "searchBox" placeholder = "Search something" autofocus />
<input type = "submit" value = "Search!" />
Depending on the browser, the placeholder text will still remain visible but the cursor will be in the box, such as for Chrome. Other browsers, such as IE 10 will place the cursor in the box but the placeholder text won't be visible. In either case, you can begin typing right away.