Well, i dunno if this is the best way to do it, but I did this once.
First formulate your SQL query:
$query = "SELECT * FROM your_table WHERE 'keyword_column' LIKE '%$criteria_entered_in_search_box_in_your_form%')" or die("Error in query");
Then run a while loop such as:
while($myrow = mysql_fetch_array($result)) { //display results here }
and that should print it out.
Like I don't know if it's the best way, but it should get you started. I used this to search through keywords on a mp3 cataloguing database.