Well, that is actually several questions in one. First, let’s discuss PHP. HTML files are just text files. They have an extension of HTML so the computer knows to send it to the browser. Once inside a brower the HTML files are interpreted and made pretty with CSS. You already probably know all this.
Any HTML page can become a PHP version just by changing it’s extension. Now, once you change the extension, it is the same page. But, now you can add PHP code to is between PHP tags. The code you place inside the tags are executed ONLY SERVER-SIDE. Then, they disappear. So, a search engine type of PHP code would use a type-in from the user and process some data in the database and then echo out a result. You would have to study the PHP code inside the blog/forum and find out where it gets it’s info from and the write some posting code either in HTML using a web form or in PHP and then send the info the the page.
This can get very complicated depending on how the forum grabs it’s info for the search engine. Quite often, they blog and forum coders think ahead and add this function to their pages. So, quite often in the docs for the forum, you can find how to do this.
Now that you understand a bit more about HTML vs. PHP, you can ask questions that might help us steer you in the correct course. First, what kind of forum are you using? What program is it if it is a canned one. And, how are you currently calling that search page. For instance, are you planning to call the page using a link on your HTML page or are you programming an actual POST to send to the page? My guess is a link on an HTML page calling a forum page?
So, hope this confuses you enough to ask some further questions. It’s all about learning here!