Hey I encountered the same problem.
I installed WordPress about a week ago, and it’s true. There is definitely no searchform.php file in the default theme.
The strange part is that there’s virtually nothing written anywhere about why it’s missing or what it contained. I solved the problem pretty much the same way, borrowing the file from someone else’s theme.
It was included in the source files of this great WordPress themebuilding tutorial:
webdesignerwall.com/tutorials/building-custom-wordpress-theme
For anyone else who is in need of it, simply copy the following text into your text editor and save it as searchform.php.
<form method="get" id="searchform" action="<?php bloginfo('url'); ?>/">
<label class="hidden" for="s"><?php _e('Search:'); ?></label>
<input type="text" value="<?php the_search_query(); ?>" name="s" id="s" />
<input type="submit" id="searchsubmit" value="GO" />
</form>
