Glasses should fit securely on the bridge of the nose, without pinching the nose. The frames should not press into the face at any point for your comfortable wearing.
If you currently wear acetate frames, your bridge measurement should be printed right on the glasses. When you moves your head, or even bends over and touches the floor, the frames should stay in place.
Your frame should rest with equal weight on your ears and nose, gripping your temples lightly. If you've tried to order glasses online, you should know your nose fit first.