
eins
one
The digit or number 1, used as a cardinal number when counting or calculating.
Wir zählen zusammen bis drei: eins, zwei, drei.
Let's count together to three: one, two, three.
one
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one
The digit or number 1, used as a cardinal number when counting or calculating.
Wir zählen zusammen bis drei: eins, zwei, drei.
Let's count together to three: one, two, three.

A grade
Informal for the school grade 'sehr gut' (very good), the best possible grade in the German school system.
Für ihren Aufsatz hat sie eine glatte Eins bekommen.
She got a straight A for her essay.

to be agreed
A fixed expression meaning that people agree or share the same opinion.
In diesem Punkt waren sich alle schnell eins.
On this point, everyone quickly agreed.

one thing
Used as an indefinite pronoun and refers to an unspecified thing, often as a substitute for 'etwas' (something) or 'eines' (one).
Wenn ich eins nicht mag, dann ist es Unehrlichkeit.
If there's one thing I don't like, it's dishonesty.
The form 'eins' with '-s' at the end is used when counting or when the number stands on its own, without a noun directly following it. It can then replace a neuter noun or be used as an abstract number.
Wir zählen jetzt: eins, zwei, drei.
We're counting now: one, two, three.
In the German school system, 'eine Eins' (an A / a 1) is the best grade ('sehr gut', very good). The expressions 'eine Eins schreiben' (to get an A / a 1 on a test) or 'eine Eins bekommen' (to get an A / a 1) are very common in everyday school language.
Er hat in der Matheprüfung eine Eins geschrieben.
He got an A on the math exam.
The expression 'sich eins sein' means 'sich einig sein' (to be in agreement) and is always used with the verb 'sein' (to be) and a reflexive form. The people who agree are in the plural.
In diesem Punkt sind wir uns zum Glück alle eins.
Fortunately, we all agree on this point.
In colloquial speech, 'eins' is often used as a pronoun for 'etwas' (something) or 'eine Sache' (one thing). It often comes at the beginning of a sentence to emphasize a particular thing.
Eins kann ich dir versprechen: Langweilig wird es nicht.
One thing I can promise you: it won't be boring.
In colloquial speech, 'eins' is often used for the time 'ein Uhr' (one o'clock). You can say both 'Es ist ein Uhr' (It is one o'clock) and 'Es ist eins' (It is one).
Wir treffen uns um eins am Bahnhof.
We're meeting at one at the train station.
a / one
Ein and eins both refer to the number 1. Ein comes before a masculine or neuter noun, while eins is used independently when counting or doing arithmetic. Before a noun, use ein; when the number stands alone, use eins.

Bitte zähle langsam: eins, zwei, drei.
Please count slowly: one, two, three.
Auf dem Tisch liegt ein Buch.
There is a book on the table.