Use vigorous up-and-down motions. The "up" stroke is actually more important for loosening the clog than the "down" stroke.
Not all plungers are equal. For a toilet, you need a (one with a fold-out rubber flap) rather than a flat sink plunger. how to fix a blocked toilet
If the plunger fails, you can try a simple chemical reaction using household items. Do not use commercial drain cleaners (like Drano) in a toilet. They can generate heat that cracks cold porcelain or damage rubber seals. Use vigorous up-and-down motions