Retrieve specific data from MySQL

Hello, I have a basic question I can't figure out. My site lets people enter in their information... I now want to be able for a user to search the database. For example, enter in "firstname" or "lastname" in a text box, hit submit, and have the results returned. How do I write this in PHP? I've tried lots of twists on SELECT * FROM table WHERE lastname=$lastname... but can't get it to work... any help greatly appreciated, thanks, Hedges