nass
wet
Covered with or soaked through with water or another liquid.
Meine Schuhe sind vom Regen komplett nass geworden.
My shoes got completely wet from the rain.

wet
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wet
Covered with or soaked through with water or another liquid.
Meine Schuhe sind vom Regen komplett nass geworden.
My shoes got completely wet from the rain.

The adjective 'nass' (wet) belongs to the word family around the noun 'die Nässe' (wetness/moisture). While 'nass' describes the state, 'die Nässe' refers to the liquid or moisture itself.
Wegen der Nässe auf dem Boden bin ich ausgerutscht.
Because of the wetness on the floor, I slipped.
To emphasize that something is very wet, colloquial intensifiers like 'klatschnass' (soaking wet), 'pitschnass' (soaking wet), or 'pudelnass' (soaking wet) are often used.
Ich bin ohne Schirm in den Regen geraten und war danach klatschnass.
I got caught in the rain without an umbrella and was soaking wet afterward.
With reference to the weather, 'nass' (wet) is often combined with 'kalt' (cold) to form 'nasskalt' (cold and damp). This word describes unpleasant, damp and cold weather that is typical of autumn or winter.
Bei diesem nasskalten Wetter möchte man am liebsten zu Hause bleiben.
In this cold, damp weather, you just want to stay at home.
The colloquial expression 'sich nass machen' (to get scared stiff / to wet oneself) is reflexive and is often combined with the preposition 'vor' (of/from) to state the reason for the fear.
Er macht sich schon vor einer kleinen Prüfung fast nass.
He practically gets scared stiff even before a small exam.
The meaning 'betrunken' (drunk) is highly colloquial and is used less often today. It usually appears in a very informal, spoken context.
Nach zehn Bier war er ziemlich nass und konnte kaum noch gerade stehen.
After ten beers, he was pretty drunk and could barely stand up straight.
blue
'blau' and 'nass' can both colloquially mean that someone is drunk. 'blau' is much better known and more natural for this meaning. 'nass' in this sense sounds rather old-fashioned or regional and can easily be misunderstood, because 'nass' normally means that something is wet. Learners may confuse the words because both can be connected with alcohol in colloquial language. In everyday use, however, 'blau' is usually the safer choice if you mean drunk.

Der alte Wirt sagte, der Gast sei gestern Abend völlig nass gewesen.
The old innkeeper said the guest had been completely drunk last night.
Nach der Feier war mein Bruder ziemlich blau.
After the party, my brother was pretty drunk.