Do you mean all the necessary checked/ticked things would have to be on each record you want from the database?
Are you searching just one table or multiple tables? If the latter you'll want to have MySQL 4.1 or higher to take advantage of Subqueries I would think.
Surely you just need to make your SELECT statement with a loop in to add a WHERE condition for each of your checked items, if it's on one table. If it's on mulitples you'll probably need to use grouping, counting, ranges and subqueries.
I think you'll need to be more specific to get the best answer.