Guidance on searching database for users

Hi
First of all the website in the link is not mine but it illustrates very nicely what I need help with.
I want to create a website where visitors can enter data (through a form) and that data gets entered into a database. Presumably MySQL is the way to go for that. Hostgator is the host. The visitor will enter 7 fields of information.
I have no idea what I should be doing to to make the visitor search work. Once the visitor enters a term they should receive a “no match found” if the there is nothing in the database. Partial matches will not be shown.
If the vistor gets a match then they should be shown 4 specific entries in the database. They won’t be able to see any other database information.

If someone can point me in the right direction I’d be very grateful. I’ll then know what I should be reading up on. A WP Plugin that is easily customisable would be even better!!

Many thanks

The page I need help with: [log in to see the link]