
nach
to
Indicates a direction or destination. Often used for cities, countries without an article, and directions like left or right.
Wir fahren morgen nach Berlin.
We're driving to Berlin tomorrow.
to / after / according to
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to
Indicates a direction or destination. Often used for cities, countries without an article, and directions like left or right.
Wir fahren morgen nach Berlin.
We're driving to Berlin tomorrow.

after
Indicates a point in time that follows another event.
Nach dem Essen gehen wir spazieren.
After the meal, we'll go for a walk.

according to
Indicates that something corresponds to a particular source, rule, or opinion; according to.
Meiner Meinung nach ist das eine gute Entscheidung.
In my opinion, that is a good decision.

after
Describes an order or sequence.
Die Schüler kamen einer nach dem anderen ins Klassenzimmer.
The students came into the classroom one after another.

like / of
Expresses that something has a certain smell, taste, or appearance.
Das riecht nach frisch gebackenem Kuchen.
That smells like freshly baked cake.

for
Used with verbs like fragen (to ask), suchen (to search), or rufen (to call) to name the target of the action.
Ich habe überall nach meinen Schlüsseln gesucht.
I searched everywhere for my keys.
The preposition 'nach' always takes the dative. Make sure to decline the noun and article after 'nach' correctly.
Nach einem langen Arbeitstag bin ich müde.
After a long workday, I'm tired.
'Nach' is used for directions to geographic destinations without an article. This applies to cities, continents, and most countries.
Im Sommer fliege ich nach Italien.
In the summer, I'm flying to Italy.
The expression 'nach Hause' (home, toward home) is a fixed exception and means movement to the place where you live. Don't confuse it with 'zu Hause' (at home), which describes being there.
Nach der Party fahre ich direkt nach Hause.
After the party, I'm going straight home.
In the meaning 'gemäß' (according to), 'nach' can also stand after the noun or pronoun it refers to. This construction is very common.
Meiner Ansicht nach sollten wir das Projekt starten.
In my view, we should start the project.
To describe a smell, taste, or impression, 'nach' is combined with verbs of perception such as 'riechen' (to smell), 'schmecken' (to taste), or 'aussehen' (to look).
Deine Hände riechen nach Seife.
Your hands smell like soap.
There are fixed verb-preposition combinations with 'nach'. Common examples are 'fragen nach' (to ask for/about), 'suchen nach' (to search for), and 'sich sehnen nach' (to long for).
Der Tourist fragte nach dem kürzesten Weg.
The tourist asked for the shortest way.
in
For destinations, nach is usually used before cities and countries without an article. in with the accusative is used especially with countries that have an article and can also emphasize entering an area. Thus, one travels nach Österreich, but in die Schweiz.

Im Sommer reisen wir nach Österreich.
We’re traveling to Austria this summer.
Im Sommer reisen wir in die Schweiz.
We’re traveling to Switzerland this summer.