
aneinander
together
Expresses that things or people are located directly next to each other, often with contact.
Die Stühle standen dicht aneinander gereiht.
The chairs were lined up close together.
together / against each other
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together
Expresses that things or people are located directly next to each other, often with contact.
Die Stühle standen dicht aneinander gereiht.
The chairs were lined up close together.

to clash
To get into an argument or conflict with each other.
Die beiden sind wegen einer politischen Meinungsverschiedenheit heftig aneinander geraten.
The two clashed fiercely over a political disagreement.

to string together
To make something follow directly after something else in a sequence or series.
Der Regisseur versteht es, spannende Szenen logisch aneinanderzureihen.
The director knows how to string exciting scenes together logically.
The word is made up of the preposition 'an' (at/on) and the reciprocal pronoun 'einander' (each other). So it literally means 'an einander' (at/on each other) or 'in contact with each other.'
Die beiden Häuser sind sehr nah aneinander gebaut.
The two houses are built very close together.
'Aneinander' is often combined with verbs of position or movement. Typical examples are 'aneinander lehnen' (to lean against each other), 'aneinander kleben' (to stick to each other), or the idiom 'aneinander vorbeireden' (to talk past each other), when two people do not understand each other.
In der vollen U-Bahn mussten die Menschen dicht aneinander stehen.
In the crowded subway, people had to stand close together.
The expression 'aneinander geraten' (to clash/get into conflict) is a fixed idiom and means to begin an argument or conflict. It is always used in this context.
Wegen einer Kleinigkeit sind die Nachbarn gestern lautstark aneinander geraten.
The neighbors got into a loud argument yesterday over a small matter.
In combination with 'reihen' (to line up), 'aneinander' forms the separable verb 'aneinanderreihen' (to string together). In a main clause, 'aneinander' stands at the end; in a subordinate clause, it stays together with the verb.
Der Autor reiht ein Klischee an das andere aneinander.
The author strings one cliché after another together.
with each other
Miteinander mainly describes a shared or reciprocal action. Aneinander, by contrast, emphasizes that people or things are directly next to each other and often touching. When the focus is on doing something together, miteinander is appropriate; when it is on immediate proximity or contact, aneinander is appropriate.

Die beiden Kinder sitzen im engen Zelt aneinander.
The two children are sitting pressed close together in the small tent.
Die beiden Kinder spielen miteinander im Garten.
The two children are playing together in the garden.