
rufen
to shout
To say or shout something in a loud voice in order to be heard.
Sie musste laut „Hilfe“ rufen, um auf sich aufmerksam zu machen.
She had to shout 'Help!' loudly to attract attention.
to call
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to shout
To say or shout something in a loud voice in order to be heard.
Sie musste laut „Hilfe“ rufen, um auf sich aufmerksam zu machen.
She had to shout 'Help!' loudly to attract attention.

to call
To summon someone or ask them to come by saying their name or using a signal.
Kannst du bitte die Kinder zum Abendessen rufen?
Can you please call the children for dinner?

to call
To summon someone or something, often by phone.
Nach dem Unfall hat jemand sofort einen Krankenwagen gerufen.
After the accident, someone immediately called an ambulance.

to launch
To found, start, or establish something new, for example a project, an organization, or an event.
Sie haben eine Initiative ins Leben gerufen, um die Umwelt zu schützen.
They launched an initiative to protect the environment.
The preposition 'nach' + dative is used to express that one wishes for or needs someone or something. 'Nach jemandem rufen' often means that you miss the person or need their help.
Das kleine Kind ruft nach seiner Mutter.
The small child is calling for his mother.
When you want to reproduce the exact words someone shouts, you often use a direct quote in the sentence. A very common fixed phrase is 'um Hilfe rufen' (to call for help).
„Vorsicht!“, rief er mir noch zu.
'Careful!' he still shouted to me.
When you ask a person to come by saying their name, that person is in the accusative. This is the most common construction in everyday life.
Ich rufe die Kinder, das Essen ist fertig.
I'm calling the children; the food is ready.
In the meaning 'bestellen' (to call/order/summon), 'rufen' is almost always used for emergency services or means of transport. Typical combinations are 'die Polizei rufen' (to call the police), 'die Feuerwehr rufen' (to call the fire department), 'einen Arzt rufen' (to call a doctor), or 'ein Taxi rufen' (to call a taxi).
Wegen des Rohrbruchs mussten wir einen Handwerker rufen.
Because of the burst pipe, we had to call a tradesperson.
The phrase 'ins Leben rufen' is a fixed expression. It is used for founding something new and positive, such as a project, an organization, or an event.
Die Bürger haben eine neue Initiative ins Leben gerufen.
The citizens launched a new initiative.
to fetch / get
When referring to a doctor, rufen mainly means contacting or summoning the doctor. Holen focuses more strongly on the doctor actually coming to the patient; it can also mean going to the doctor and bringing him along.

Ich rufe telefonisch einen Arzt für den verletzten Mann.
I call a doctor by phone for the injured man.
Ich hole den Arzt aus dem Behandlungszimmer zum verletzten Mann.
I fetch the doctor from the treatment room for the injured man.