kleben
to glue
To attach something to another thing using an adhesive.
Ich muss das Poster wieder an die Wand kleben.
I need to glue the poster back onto the wall.

to stick / to glue
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to glue
To attach something to another thing using an adhesive.
Ich muss das Poster wieder an die Wand kleben.
I need to glue the poster back onto the wall.

The verb 'kleben' (to stick / to glue) is often used with the preposition 'an' (on/to). The accusative indicates direction (where to?), while the dative describes a fixed location (where?).
Er klebt den Zettel an die Tür.
He glues the note to the door.
Pay attention to the subject of the sentence. If a person is the subject, 'kleben' usually means an active action. If a sticky substance is the subject, it describes a property.
Die Kinder kleben bunte Bilder in ihr Heft.
The children glue colorful pictures into their notebook.
In the colloquial meaning, 'kleben' is often used figuratively. Typical expressions are 'an jemandes Lippen kleben' (to hang on someone's every word) or 'am Bildschirm kleben' (to be glued to the screen).
Die Kinder klebten an seinen Lippen, als er die Geschichte erzählte.
The children hung on his every word as he told the story.
This meaning is very new and is found almost exclusively in the context of climate activism and civil disobedience. The activists are often referred to as 'Klimakleber' (climate gluers).
Die Demonstranten drohten damit, sich auf der Autobahn festzukleben.
The demonstrators threatened to glue themselves to the highway.
In the meaning 'sich aus Protest festkleben' (to glue oneself in place in protest), the verb is always used reflexively with 'sich'. It is usually followed by the preposition 'an' or 'auf' with the dative.
Einige Aktivisten haben sich an einem berühmten Gemälde festgeklebt.
Some activists glued themselves to a famous painting.
to attach / bring up
'anbringen' and 'kleben' can both mean that something is attached to a surface. 'kleben' says more precisely how this happens: with glue or because something is sticky. 'anbringen' is more general and can also involve screws, nails, or other means. Learners may confuse the words when, for example, a poster goes on the wall. If glue is important, 'kleben' sounds more natural; if the type of attachment is not important or something is being mounted, 'anbringen' fits better.

Für die Party klebt Lena bunte Sterne an die Fenster.
For the party, Lena sticks colorful stars to the windows.
Die Hausmeisterin bringt im Eingang ein neues Namensschild an.
The caretaker attaches a new nameplate in the entrance.