Question

I was wondering how to make a Wikipedia search gadget in HTML code. This gadget is for a personal blog that I am working on.

Answer 1

Build a form redirecting on submit or load the target page via ajax etc.

http://en.wikipedia.org/w/index.php?title=Spezial%3ASuche&search=%s

Where %s is your search query. Like:
http://en.wikipedia.org/w/index.php?title=Spezial%3ASuche&search=test

<form method="GET" action="http://en.wikipedia.org/w/index.php">
    <input type="hidden" name="title" value="Spezial%3ASuche" />    
    <input type="text" name="search" />
    <input type="submit" value="Search" />
</form>

Sample
http://jsfiddle.net/CkK3j/