Finally got this DS18B20 working. Actually three of them. And in two modes. Parasite power mode and main mode.
A 4.7K ohm resistor is the key.
Starting with the main mode, three wires are needed, as this sensor has three pins.
Datasheet is here http://datasheets.maxim-ic.com/en/ds/DS18B20.pdf.
Connection is almost simple.
Pin 1 to Arduino ground
Pin 2 to Arduino digital input
Pin 3 to Arduino 5V
And a 4.7K resistor between pin 2 and pin 3
Works with three wires, as seen on the followind illustration.