You might receive better answers if you could include more detail in your question (i.e. what information, code, etc. you already have).
If you have a database table set up...something with a column for each search criteria, for example, then you could use a simple SQL query to extract the rows containing the Teachers you need. For example:
$instrument='drum';//or whatever valid input you received from the user's search
$postalCode='12345';//or whatever valid input you received from the user's search
mysql_query("SELECT `teachers`.* FROM `teachers` WHERE `instrument`='$instrument' AND `postalCode`='$postalCode'");
BE SURE TO CLEAN YOUR VARIABLES (i.e. use htmlentities($instrument,ENT_QUOTES, 'utf-8') ) before using the variable in your SQL to prevent SQL injection attacks.
Alternately, you could select all teachers from the database or in an array and loop through the array extracting the information which meets the user's search criteria. While this approach is probably less likely to be a threat to your database, it is resource intensive.