You can still buy a "dagkaart" and have it loaded on an anonymous OV-Chipkaart. A 2nd class day card costs € 51. It gives free train travel for a whole day (technically, until 4AM the morning after you first validate it).
You need to check-in and check-out on totems or gates when you are taking your trips, you can't just check-in early in the morning and forget about checking out until you are done for the day, this will yield you a fine for improper use. So check-in and check-out everytime you complete a journey.
The public transportation day pass that gave unlimited national-wide rides on both trains and local trams/buses/subways has been abolished.