i understand that both of these castles are close to each other. I dont have a car, any suggestion on how to get from Karlstein to Krivoklat(or vise versa)via public transport on a day trip from Prague. I am not really interested in taking a tour.
Thank you

These castles are really close to each other. For your information: Prague - Karlstejn approx. 25 miles, Karlstejn - Krivoklat approx. 20 miles and Krivoklat - Prague approx. 35 miles.
There is no problem with the train from Prague to Karlstejn (and vice versa).
Then you can go on by train from Karlstejn to Krivoklat (you have to change trains in the city of Beroun). From Krivoklat to Prague you can use also the train (you will have to change trains in the city of Beroun as well).
There is a time table you can use:

From Monday to Friday
Departure time 8:11 Prague, station Hlavni nadrazi - Arrival time 8:55 Karlstejn
Departure time 12:55 Karlstejn - Arrival time 13:04 Beroun
Departure time 13:48 Beroun - Arrival time 14:33 Krivoklat
Departure time 18:43 (or 20:51) Krivoklat - Arrival time 19:30 (or 21:28) Beroun
Departure time 19:34 (or 21:34) Beroun - Arrival time 20:29 (or 22:29) Prague, station Hlavni nadrazi

On Saturdays and Sundays
Departure time 8:11 Prague, station Hlavni nadrazi - Arrival time 8:55 Karlstejn
Departure time 14:25 Karlstejn - Arrival time 14:34 Beroun
Departure time 14:42 Beroun - Arrival time 15:36 Krivoklat
Departure time 18:43 (or 20:51) Krivoklat - Arrival time 19:30 (or 21:28) Beroun
Departure time 19:34 (or 21:34) Beroun - Arrival time 20:29 (or 22:29) Prague, station Hlavni nadrazi

I'll thank Milan1963 for the thoroughness of this response in case someone else doesn't.

Milan1963, are you the tour guide Dana?

No, I am not a tour guide Dana.