stoßen
to bump / push
To push, hit, or ram someone or something with a short, forceful movement.
Pass auf, dass du nicht gegen den Tisch stößt.
Be careful not to bump into the table.

to push / bump / come across
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to bump / push
To push, hit, or ram someone or something with a short, forceful movement.
Pass auf, dass du nicht gegen den Tisch stößt.
Be careful not to bump into the table.

The verb 'stoßen' (to push/bump) can be used with 'haben' or 'sein'. 'Haben' is used for the active action (intentionally pushing someone). 'Sein' is used for an unintentional collision or a chance discovery.
Er hat seinen Gegner zu Boden gestoßen.
He pushed his opponent to the ground.
The meaning of 'stoßen' changes completely depending on the preposition. Pay close attention to whether the verb is combined with 'auf', 'zu', or 'an', because this creates completely new, figurative meanings.
Wir sind bei der Wanderung auf eine seltene Pflanze gestoßen.
We came across a rare plant during the hike.
When you accidentally injure yourself, a special reflexive construction is used. The person is in the dative, and the body part is in the accusative: 'sich (dative) + Körperteil (body part, accusative) + stoßen' (to bump a body part).
Ich habe mir den Ellbogen am Tisch gestoßen.
I bumped my elbow on the table.
The expression 'auf etwas stoßen' (to come across something / meet with something) is very often used figuratively. Typical combinations are 'auf Widerstand stoßen' (to meet with resistance), 'auf Kritik stoßen' (to meet with criticism), or 'auf Zustimmung stoßen' (to meet with approval).
Sein Vorschlag stieß im Team auf große Begeisterung.
His suggestion met with great enthusiasm in the team.
When you join a group that is already there, you use the fixed expression 'zu jemandem/etwas stoßen' (to join someone/something). The separable verb 'dazustoßen' (to join in / join later) is often used for this as well.
Wir sitzen schon im Café, du kannst einfach zu uns stoßen.
We're already sitting in the café; you can just join us.
The meaning 'angrenzen' (to border on) is used almost exclusively in a spatial or geographic context to describe the boundaries of properties, gardens, or countries.
Unser Garten stößt an ein kleines Waldstück.
Our garden borders on a small piece of woodland.
The meaning 'zerkleinern' (to crush) is specific to cooking or pharmacy. It is used when you crush hard ingredients such as spices, herbs, or nuts in a mortar.
Für das Curry müssen die Gewürze frisch gestoßen werden.
For the curry, the spices must be freshly crushed.
to find
'finden' and 'auf etwas stoßen' can both mean that you discover something. 'finden' is the normal, very general word: you can find something after searching or by chance. 'auf etwas stoßen' is used more when you discover something unexpectedly, often during a search, research, or investigation. It sounds a little more figurative and less everyday than 'finden'. They can be confused because both describe a result. In practice: for normal things like keys, a phone, or an address, 'finden' is usually more natural. For information, clues, or problems, 'auf etwas stoßen' often fits better.

Bei der Vorbereitung stößt sie auf einen Fehler im Vertrag.
During the preparation, she comes across an error in the contract.
Nach zehn Minuten finde ich endlich meinen Schlüssel in der Jacke.
After ten minutes, I finally find my key in my jacket.