As defined in Wikipedia, a separable verb is a verb that is composed of a core verb and a separable particle. In some sentence positions, the core verb and the particle appear in one word, while in others the core verb and the particle are separated.

The word ein in German can be the particle of a separable verb, or the indefinite article "a" or "an." It is sometimes difficult to see in a sentence which one it is. It will help you to distinguish ein- as a prefix particle of a separable verb if you learn some of the separable verbs starting with ein-.

Many German verbs start with the particle ein. This is because in English, you may "drill into a wall," and "into" is a preposition. But in German, the "into" is  part of the verb: "to drill" is bohren, but "to drill into" is einbohren. Thus there are hundreds of verbs starting with ein-, but let's concentrate today on the more common ones. The present tense is shown additionally for examples that aren't in their "separated" form.

Er atmete tief ein und spielte eine einzige Note.

He took a deep breath and played a single note.

Caption 38, Märchen - Sagenhaft - Der Rattenfänger von Hameln

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Ne, wenn man hier Magnete einbauen würde...

Right, if you were to install magnets here...

Caption 69, Das 1. Newtonsche Gesetz - erklärt am Beispiel des Dodomobils

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Present tense: Man baut die Magnete ein.

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Sollen wir nächste Woche ein Meeting einberufen?

Should we call a meeting for next week?

Caption 10, Berufsleben - Probleme mit Mitarbeitern

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Present tense: Wir berufen ein Meeting ein.

Du bildest dir doch wohl nicht ein, dass du da hingehst?

Surely you don't actually imagine that you're going there?

Caption 21, Märchenstunde - Das Aschenputtel

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Der zeigt, dass das Eis elastisch ist

It shows that the ice is elastic

und nicht plötzlich einbrechen kann.

and can't suddenly collapse.

Captions 43-44, Unterwegs mit Cettina - Schlittschuhlaufen

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Present tense: Das Eis bricht nicht plötzlich ein.

Further Learning
Go to Yabla German and read these three lessons about separable verbs in German. Then see if you can find some Yabla videos that use the following verbs with the ein- particle: einarbeiten, einbilden, einchecken, einkaufen, einkommen, einladen, einloggen, einpacken, einreisen, einschlafen, einstellen, einstufen, eintippen, einwandern, einzahlen.