This is pretty much the method to do this. You'll need to create four files.
Create a database and a table for your text data.
Create a query to extract the data you require. Save to a single php file.
Create a query to insert the data you want to insert. Save to a separate php file.
Create your HTML page including the web form. To keep things simple divide the page into a 60/40 split placing the web form in the 40 split. You'll need to add a php include to the select query php file in the 60 split. Save as index.html.
Create a formhandler php script. This goes into the action="" part of the web form and is called when the person clicks submit. This script needs to validate all data has been correctly entered from the web form and is safe for inserting into your db. When you get to the point you want to insert the data then include insert query php file. Then at the end add a header(); function to return the user back to the index page without them realising it. This will also refresh the page with the data they added.
Note that there should be no HTML on this page at all. if there is then the header() functions won't work.
// Display success message.
header('Location: contact-success.html');
When I want to do a contact form handler I usually add a conditional at the end that throws the user either back to an error page or a success page. You could always provide a variable with an error value that allows you to customise explanations to the user as to why their entry wasn't accepted.
This is a fairly simple way to do this and takes no account of the need to approve data as it's submitted before it goes live. Take a close look at form validation (on this site and others) as well as techniques for safely inserting data into a db (eg addslashes()).