rühren
to stir
To put a liquid or mixture into a circular motion with a spoon or similar object in order to mix the ingredients.
Du musst die Soße ständig rühren, damit sie nicht anbrennt.
You have to stir the sauce constantly so it doesn't burn.

to stir / move
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to stir
To put a liquid or mixture into a circular motion with a spoon or similar object in order to mix the ingredients.
Du musst die Soße ständig rühren, damit sie nicht anbrennt.
You have to stir the sauce constantly so it doesn't burn.

Pay attention to whether the verb is used reflexively. 'Etwas rühren' means to stir a liquid. 'Sich rühren' means to move or to take action.
Ich rühre den Zucker in meinen Tee.
I stir the sugar into my tea.
When 'rühren' (to move) touches someone emotionally, the person is the accusative object of the sentence. A very common expression in this context is 'jemanden zu Tränen rühren' (to move someone to tears).
Der Film hat das Publikum tief gerührt.
The film deeply moved the audience.
In the kitchen, 'rühren' (to stir) is often used with the prepositions 'in' (in/into) or 'unter' (into/through) to mix ingredients. Typical objects are 'Soße' (sauce), 'Suppe' (soup), 'Teig' (dough/batter), or 'Kaffee' (coffee).
Rühre bitte die Kräuter unter den Quark.
Please stir the herbs into the quark.
In the meaning 'sich bewegen' (to move), 'sich rühren' is very often negated to express that someone or something is completely still.
Der Hund lag in der Sonne und rührte sich nicht.
The dog lay in the sun and did not move.
When 'sich rühren' means 'aktiv werden' (to take action), it often describes a lack of response in a situation that requires action. It has a slightly moral or social connotation.
Obwohl alle die Ungerechtigkeit sahen, rührte sich niemand zum Protest.
Although everyone saw the injustice, no one took action to protest.
to act / trade
'handeln' and 'sich rühren' can both mean that someone becomes active. 'handeln' is more neutral and more general: someone does something, often in response to a problem. 'sich rühren' sounds more colloquial and emphasizes that someone finally does something or shows initiative. It is often used when nothing had happened before or when you are urging someone to act. 'handeln' fits many factual situations, while 'sich rühren' fits more in everyday language and when there is slight pressure: now someone has to do something.

Nach der dritten Erinnerung rührt sich der Vermieter endlich.
After the third reminder, the landlord finally takes action.
Nach der Warnung der Polizei handelt die Stadt und sperrt die Straße.
After the police warning, the city takes action and closes the road.