stürzen
to fall
To lose one's balance and fall to the ground, usually unintentionally.
Sei vorsichtig auf dem nassen Boden, damit du nicht stürzt.
Be careful on the wet floor so you don't fall.

to fall / overthrow
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to fall
To lose one's balance and fall to the ground, usually unintentionally.
Sei vorsichtig auf dem nassen Boden, damit du nicht stürzt.
Be careful on the wet floor so you don't fall.

The perfect tense of 'stürzen' is formed with 'sein' when it describes movement or falling. In other meanings, such as overthrowing a government or emptying a container, 'haben' is used.
Der Radfahrer ist auf der glatten Straße gestürzt.
The cyclist fell on the slippery road.
'Stürzen' is often used reflexively with 'sich' (oneself). The pronoun 'sich' is in the accusative and indicates that the action is directed back at the subject itself.
Er stürzte sich in die Arbeit, um sich abzulenken.
He threw himself into work to distract himself.
The verb 'stürzen' is closely related to the noun 'der Sturz' (fall/overthrow). 'Der Sturz' can mean both falling (a fall from a bicycle) and an overthrow (the fall of the government), which connects the different meanings of the verb.
Nach dem Sturz hatte er Schmerzen im Knie.
After the fall, he had pain in his knee.
In the political meaning, 'stürzen' is always used with an accusative object that describes a person or institution in a position of power.
Die Demonstranten forderten, den Präsidenten zu stürzen.
The protesters demanded that the president be overthrown.
The expression 'sich stürzen auf' (to pounce on) always requires the preposition 'auf' followed by the accusative. It describes a quick, greedy, or very eager movement toward a target.
Die Journalisten stürzten sich auf den berühmten Schauspieler.
The journalists pounced on the famous actor.
The expression 'sich stürzen in' (to throw oneself into) uses the preposition 'in' with the accusative. It means that someone devotes themselves to a new activity, work, or adventure with full energy.
Nach der Schule stürzte er sich in sein Studium.
After school, he threw himself into his studies.
In the context of cooking and baking, 'stürzen' has a very specific meaning: you carefully turn a cake or pudding out of its mold.
Nach dem Backen muss man den Kuchen auf ein Gitter stürzen.
After baking, you have to turn the cake out onto a wire rack.
to fall
'fallen' and 'stürzen' both describe a downward movement, often all the way to the ground. 'fallen' is the more general word: a glass, a leaf, or a person can fall. 'stürzen' is used especially when a person loses their balance and may get injured, or when something falls from a great height. It sounds stronger and more dramatic than 'fallen'. Learners may confuse the words because both fit in accidents. As a simple guide: 'fallen' is more neutral, while 'stürzen' emphasizes the accident or danger.

Auf der nassen Treppe stürzt Leon und verletzt sich am Knie.
Leon falls on the wet stairs and injures his knee.
Beim Aufräumen fällt mir ein Buch aus dem Regal.
While tidying up, a book falls off the shelf.