Correct design for quering DB through out the app

I want to use sqlite driver for my java application that I am developing with netbeans. What would be the correct "design" when it comes to integrating DB querys? Basically should I create a static variable holding the connection which I can use to execute sql statements through out the app? Or should I create the connection everytime I want to do the query? Here is m code

  Class.forName("org.sqlite.JDBC"); 
    conn = DriverManager.getConnection("jdbc:sqlite:Mydb.db");
    st = conn.createStatement();
    rs = st.executeQuery(/*My sql statement*/);

Thank you