einziehen
to move in
To take up residence in a new apartment or a new house.
Nächste Woche ziehen wir endlich in die neue Wohnung ein.
Next week we are finally moving into the new apartment.

to move in / collect / absorb
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to move in
To take up residence in a new apartment or a new house.
Nächste Woche ziehen wir endlich in die neue Wohnung ein.
Next week we are finally moving into the new apartment.

'Einziehen' (to move in / collect / absorb) is a separable verb. The prefix 'ein-' stands at the end of the main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Meine neuen Nachbarn ziehen morgen ein.
My new neighbors are moving in tomorrow.
The verb consists of 'ein-' (in, into) and 'ziehen' (to move, to pull something). The literal meaning 'hineinziehen' (to pull into) or 'hineinbewegen' (to move into) helps you understand many of the figurative meanings, e.g. into an apartment, into the skin, or into an organization.
Die Soldaten zogen in die eroberte Stadt ein.
The soldiers entered the conquered city.
The perfect tense is formed with 'sein' (to be) when movement of the subject is meant, e.g. moving into a house or cream being absorbed. In the other meanings, such as money, driver's license, or military, 'haben' (to have) is used.
Wir sind letztes Jahr in dieses Haus eingezogen.
We moved into this house last year.
When someone moves into a new place to live, the preposition 'in' is used with the accusative. Typical formulations are 'in eine Wohnung einziehen' (to move into an apartment) or 'in ein Haus einziehen' (to move into a house).
Sie ist gerade in ihre erste eigene Wohnung eingezogen.
She has just moved into her first apartment of her own.
In this meaning, 'einziehen' (to collect) is usually combined with financial or administrative terms. Typical objects are 'Schulden' (debts), 'Steuern' (taxes), 'Gebühren' (fees), or 'Forderungen' (claims).
Das Finanzamt wird die ausstehenden Steuern einziehen.
The tax office will collect the outstanding taxes.
In the meaning 'absorbiert werden' (to be absorbed), the verb is often used without an object. The subject is the substance that penetrates into a surface.
Die Sonnencreme zieht schnell ein und fettet nicht.
The sunscreen absorbs quickly and is not greasy.
This meaning is typical of official language. The subject is usually an authority such as the police or customs, which officially takes something away.
Der Zoll hat die gefälschten Markenprodukte eingezogen.
Customs confiscated the counterfeit branded products.
In the context of military service, 'einziehen' (to draft) is very often used in the passive to say that someone was required to serve. The construction is: 'jemand wird (zum Militär) eingezogen' (someone is drafted into the military).
Er wurde direkt nach der Schule zum Wehrdienst eingezogen.
He was drafted into military service right after school.
to refer / move into / receive
'beziehen' and 'einziehen' can both mean that you move into a new apartment or house. 'einziehen' is very common for this in everyday language and emphasizes the act of moving. 'eine Wohnung beziehen' (to move into an apartment) also means to begin living there, but it sounds somewhat more formal, for example in contracts, advertisements, or official texts. The words can be confused because they are almost the same in this meaning. In conversation, people usually say 'einziehen'; in more formal texts, 'beziehen' fits well.

Lea zieht heute in ihre erste eigene Wohnung ein.
Lea is moving into her first apartment of her own today.
Die Familie bezieht im September eine größere Wohnung.
The family is moving into a larger apartment in September.