faul
lazy
Work-shy and sluggish; not wanting to make an effort or be active.
Am Sonntag bin ich meistens faul und liege den ganzen Tag auf dem Sofa.
On Sundays, I'm usually lazy and lie on the sofa all day.

lazy / rotten
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lazy
Work-shy and sluggish; not wanting to make an effort or be active.
Am Sonntag bin ich meistens faul und liege den ganzen Tag auf dem Sofa.
On Sundays, I'm usually lazy and lie on the sofa all day.

The meaning of 'faul' (lazy / rotten) depends heavily on the context. If it refers to a person or an animal, it means 'sluggish' or 'work-shy'. If it refers to food or organic material, it means 'spoiled' or 'rotten'.
Mein Kater ist sehr faul und schläft den ganzen Tag.
My tomcat is very lazy and sleeps all day.
A very common idiom is 'auf der faulen Haut liegen'. It means that someone is inactive and does nothing, that is, lazes around.
Am Wochenende will ich einfach nur auf der faulen Haut liegen und entspannen.
At the weekend, I just want to laze around and relax.
The meaning 'verdorben' (spoiled) is related to the noun 'die Fäulnis' (rot/decay). 'Fäulnis' describes the process of decomposition. This helps you remember the meaning for food.
Durch die Feuchtigkeit im Keller begann das Holz in die Fäulnis überzugehen.
Because of the moisture in the basement, the wood began to rot.
The phrase 'an der Sache ist etwas faul' (there is something fishy about the matter) is used to express mistrust. It means that a situation seems suspicious or something is not right.
Er hat mir ein zu gutes Angebot gemacht. Ich glaube, an der Sache ist etwas faul.
He made me an offer that was too good. I think there is something fishy about it.
In the meaning 'unehrlich' (dishonest) or 'schlecht' (bad), 'faul' is often combined with abstract nouns. Typical examples are 'eine faule Ausrede' (a lame excuse) or 'ein fauler Kompromiss' (a poor compromise).
Er sagte, er hätte den Bus verpasst, aber das war nur eine faule Ausrede.
He said he had missed the bus, but that was just a lame excuse.
fresh
'frisch' and 'faul' form a clear contrast when talking about food. 'Frisch' says that something is still good because it was harvested, bought, or prepared recently. 'Faul' says that something has spoiled through decomposition and should no longer be eaten. Important: 'faul' can also describe a person who does not want to work, but in this contrast it is about spoiled food. With food, the simple rule is: fresh is good and edible; rotten is spoiled.

Wirf die Tomate weg, sie ist schon faul.
Throw the tomato away; it's already rotten.
Auf dem Markt kauft Maria frisches Obst für das Wochenende.
At the market, Maria buys fresh fruit for the weekend.