[nameless]

Hey, I use to use the forums regularily a few years ago but since then I kinda stopped coding and started pursuing other projects.
Anyways a new website fell into my lap that I am making for someone and I need to write a search function that basically allows the user to search my mysql database for a name - first and last.

What I dont get and I might have my database set up wrong, but I have the first and last name in different fields, and if a user searches for a full name, what would be the easy way for my search code to find it? What if they only enter half the name etc?
I am sure it is a pretty simple concept just my brain has frozen up on me.

Thanks,

Trevor