There are two ways add search box into your blogger blog.
1. Blogger Widget
Steps to add this search box
(i) From Dashboard, Go to Layout
(ii) Add Page Element
(iii) Select HTML/JavaScript, Name it Search Box and add this code.
<p align="center"><form id="searchthis" action="/search" style="display:inline;" method="get"> <input id="search-box" name="q" size="18" type="text"/> <p align="center"><input id="search-btn" value="Search" type="submit"/></p> </form></p>
(iv) Place it wherever you want to and you are done
2. Google Custom Search Engine
Another very advantageous method is to add a Google Custom Search Engine to your blog for free.
. The advantages:
1. Include one website, multiple websites, or specific webpages.
2. Host the search box and results on your own website.
3. Customize the colors and branding to match your existing webpages.
To create your custon Search Engine Click here http://www.google.com/coop/cse/