die Seite
page
One of the two surfaces of a flat object, especially a sheet of paper in a book, newspaper, or magazine.
Schlagen Sie bitte die Seite 42 im Buch auf.
Please open the book to page 42.

page / side
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page
One of the two surfaces of a flat object, especially a sheet of paper in a book, newspaper, or magazine.
Schlagen Sie bitte die Seite 42 im Buch auf.
Please open the book to page 42.

The preposition changes depending on whether a position (Wo? — where?) or a direction (Wohin? — to where?) is being described. You are 'auf einer Seite' (on one side; dative), but you go 'zur Seite' (to the side) or put something 'auf die Seite' (to the side; accusative).
Die Toiletten finden Sie auf der rechten Seite.
You will find the restrooms on the right side.
To distinguish the many meanings, pay attention to the context. Numbers and the word 'Buch' (book) point to a book page, 'Internet' to a web page, and 'Streit' (argument) to a party in a conflict.
Schlagen Sie bitte Seite 25 auf.
Please open to page 25.
The fixed expression 'jemandem zur Seite stehen' means to support a person. The person receiving the support is always in the dative.
In dieser schweren Zeit stand ihm seine Familie fest zur Seite.
During this difficult time, his family stood firmly by him.
In connection with books or documents, 'Seite' (page) is often used with the verbs 'aufschlagen' (to open), 'umblättern' (to turn the page), or 'lesen' (to read).
Er blätterte eine Seite um und las weiter.
He turned a page and kept reading.
When a web page is meant, typical verbs are 'besuchen' (to visit), 'aufrufen' (to open/access), or 'finden' (to find). The preposition 'auf' (on) is often used.
Auf dieser Seite können Sie sich für den Newsletter anmelden.
On this page, you can sign up for the newsletter.
To describe an aspect of someone's personality, 'Seite' (side) is often combined with a possessive pronoun and an adjective. Typical examples are 'seine lustige Seite' (his funny side) or 'ihre ernste Seite' (her serious side).
Er hat eine sehr ehrgeizige Seite, die nicht jeder kennt.
He has a very ambitious side that not everyone knows about.
party / party to
'die Seite' and 'die Partei' can both refer to people or groups in a dispute, contract, or conflict. 'Seite' is more general here: you stand on someone's side, or one side has an opinion. 'Partei' is more specific when it is about a person or group involved in a legal dispute, contract, or conflict. In the phrase 'Partei ergreifen' (to take sides), it means something similar to: to place yourself on one side. Learners may confuse the words because both occur in conflicts. For a position in an argument, 'Seite' often sounds more natural; for official or legal participants, 'Partei' fits better.

In der Diskussion stellte sich Maria auf die Seite ihrer Schwester.
In the discussion, Maria took her sister's side.
Vor Gericht musste jede Partei ihre Unterlagen vorlegen.
In court, each party had to present its documents.