How to execute a shell script from a web page or application

i'm developing a web application for acomplish the next:

1. Fill a form with the date (day and month) using a web page. I can use PHP to achieve that.

2. Use the data as an input for a linux shell script for search data among a large text file.

How can you connect html with your server for execute a shell script?

3. Graph the data in the web page.

I made an html code who can achieve that, but, i need to "rewrite" the html code or use the output of the shell script?

Can you give me advices or ideas to achieve the objectives?

Thanks in advance