trouble with MySQL 'LIKE' command

I'm trying to implement a search on my site. When the user enters a search string and pressed the Search button it sends the search string into a cariable I call searchfor, and I then construct a query that goes something like : "SELECT <whatever> FROM <a table> WHERE product_name LIKE $searchfor..... now I know there are things you can do with LIKE such as '%' to search for an arbitrary number of characters before or after the search string. 'WHERE product_name LIKE '%$searchfor%'....' this has been causing me problems by outputting mostly rubbish, and then I find out that the '$' is used in the LIKE command for matching characters too. How do I construct a SELECT statement that uses a PHP variable in the LIKE clause?