klein
small
Of small size, extent, or dimension. The opposite of 'groß' (big).
Wir wohnen in einem kleinen Haus am Stadtrand.
We live in a small house on the outskirts of town.

small
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small
Of small size, extent, or dimension. The opposite of 'groß' (big).
Wir wohnen in einem kleinen Haus am Stadtrand.
We live in a small house on the outskirts of town.

When 'klein' (small) is used like a noun, it is capitalized. This often happens after articles ('der Kleine' - the little one, 'die Kleinen' - the little ones) or indefinite pronouns ('etwas Kleines' - something small, 'nichts Kleines' - nothing small).
Die Großen passen auf die Kleinen auf.
The big ones look after the little ones.
There is a difference between 'klein schreiben' (to write in small handwriting or small font size) and 'kleinschreiben' (to write a letter as lowercase, not as a capital letter).
Du schreibst so klein, ich kann es kaum entziffern.
You write so small, I can barely decipher it.
The phrase 'als ich klein war' (when I was little/young) is a very common way to talk about one's own childhood. 'Klein' means 'young' here.
Als ich klein war, bin ich oft auf Bäume geklettert.
When I was young, I often climbed trees.
In the meaning 'unimportant', 'klein' is often combined with abstract nouns. Typical examples are: 'ein kleines Problem' (a minor problem), 'ein kleiner Fehler' (a minor mistake), 'eine kleine Sorge' (a small worry), or 'nur eine kleine Sache' (only a small thing).
Das ist nur ein kleiner Fehler, den wir schnell beheben können.
That's only a minor mistake that we can fix quickly.
The idiom 'von klein auf' means 'since early childhood'. It is used to emphasize that an ability or habit began very early in life.
Er kann von klein auf Ski fahren.
He has been able to ski since early childhood.
The expression 'klein beigeben' is a fixed phrase with the separable verb 'beigeben'. It means that one gives up one's resistance.
Er wollte zuerst nicht nachgeben, aber am Ende gab er doch klein bei.
At first he didn't want to give in, but in the end he did give in.
'Das Kleingedruckte' (the fine print) is a fixed term. It refers to the part of a text that is written in small print and often contains important details. 'Gedruckte' is a participle used as a noun here.
Es ist immer ratsam, vor dem Unterschreiben das Kleingedruckte zu lesen.
It is always advisable to read the fine print before signing.
big / great
'groß' and 'klein' are opposites in several important areas. For things or people, 'groß' describes a large extent or height, while 'klein' describes a small size. With children and age, 'klein' can mean young, while 'groß' can also mean grown-up or older. There is also an opposition in importance: 'eine große Aufgabe' is important or significant, while 'eine kleine Sache' is rather unimportant. So the exact meaning depends on the noun these words are used with.

Am Bahnhof kaufte Lena eine kleine Flasche Wasser für die Reise.
At the train station, Lena bought a small bottle of water for the trip.
Für das neue Sofa brauchen wir ein großes Auto.
We need a large car for the new sofa.