Virtism

To  Add google search to your website , first you need to understand , how does google execute it's site specific query . 

If we had to search only one site , e.g. virtism.com for keywords "best web design" .Following query will make google search work . 

http://www.google.com/search?q=best web design&sitesearch=virtism.com 

we're providing this query with two elements

1) Search String : q=best web design

2) domain to search: sitesearch=virtism.com

Making the Form :

 If you understand the above two things , rest is straight forward  

 All you need to do is create a form which will pass these values ( 1 and 2 ) , action of form will contain action="http://www.google.com/search"