
einrichten
to furnish
To equip a room or apartment with furniture and other objects.
Nach dem Umzug müssen wir unsere neue Wohnung noch komplett einrichten.
After the move, we still have to completely furnish our new apartment.
to furnish / set up
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to furnish
To equip a room or apartment with furniture and other objects.
Nach dem Umzug müssen wir unsere neue Wohnung noch komplett einrichten.
After the move, we still have to completely furnish our new apartment.

to set up
To organize, install, or create something so that it can be used, e.g. an account, a connection, or an institution.
Der Techniker kommt morgen, um den Internetanschluss einzurichten.
The technician is coming tomorrow to set up the internet connection.

to prepare for
To prepare for and adjust to a specific situation or future development.
Wegen des angekündigten Streiks müssen wir uns auf längere Wartezeiten einrichten.
Because of the announced strike, we have to prepare for longer waiting times.

to set
In medicine, to bring the parts of a broken bone or a dislocated joint back into the correct position.
Der Arzt musste den gebrochenen Arm des Jungen sofort einrichten.
The doctor had to set the boy's broken arm immediately.
'Einrichten' (to furnish / set up) is a separable verb. The prefix 'ein-' stands at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Sie richtet ihre neue Wohnung modern ein.
She furnishes her new apartment in a modern style.
The object of the sentence reveals the meaning: if you 'einrichten' (furnish) a 'Wohnung' (apartment) or a 'Zimmer' (room), it is about furniture. If you 'einrichten' (set up) a 'Konto' (account) or 'WLAN' (Wi-Fi), it is about technology. If you 'einrichten' (set) a 'Knochen' (bone), it is medical.
Wir müssen noch das Kinderzimmer einrichten.
We still have to furnish the children's room.
When furnishing rooms, adverbs are often used to describe the style. Typical combinations are 'gemütlich einrichten' (to furnish cozily), 'modern einrichten' (to furnish in a modern style), or 'neu einrichten' (to refurnish / furnish anew).
Sie haben ihr Wohnzimmer sehr gemütlich eingerichtet.
They furnished their living room very cozily.
In this meaning, the verb is always reflexive and is used with the preposition 'auf' and the accusative: 'sich auf etwas einrichten' (to prepare for something). It means to prepare mentally or organizationally.
Wegen des Staus sollten wir uns auf eine längere Fahrt einrichten.
Because of the traffic jam, we should prepare for a longer drive.
to found / be based on
Gründen emphasizes that an independent organization or institution comes into being. Einrichten emphasizes the practical or organizational provision of something so that it can be used. Thus, for example, one founds an association and sets up a counseling center within its work.

Der neue Verein richtet eine telefonische Beratungsstelle für ältere Menschen ein.
The new association is setting up a telephone counseling center for older people.
Die Helfer gründen einen Verein zur Unterstützung älterer Menschen.
The volunteers are founding an association to support older people.