adding searchbox to your blogspot template

Open your template ,and insert this code where you want searchbox appear :

<form id='searchThis' action='search' method='get'><input id='searchBox' name='q' type='text'> <input id='searchButton' value='Go' type='submit'></form>

Another way easier . You can insert a Html/javascript widget in your site and paste the code above in the content of widget .
You can customize how searchbox look by adding some CSS 
Done !