• Raspberry Pi running Raspbian Jessie with display, mouse, keyboard and power source (see Introduction, steps 1-5)
  • USB wifi dongle (not required for the Raspberry Pi 3)
  • only for the Raspberry Pi Zero: micro-USB to USB adapter
  • Wifi network (WPA) or smartphone with internet connection

Before setting up a wifi connection, you need to setup and configure your Raspberry Pi with Raspbian Jessie like shown in the steps 1-5 in the Introduction.
For wifi, all Raspberry Pis except the Raspberry Pi 3, who comes with onboard wifi, need an USB wifi adapter; the Raspberry Pi Foundation build one optimized for the Raspberry Pi (official wifi dongle). The RPI Zero needs an additional micro-USB to USB adapter.

Smartphone Tethering
This step is only necessary if you don’t have access to a wifi network already!
Smartphones with internet connection are capable of sharing their internet access as a mobile hotspot (tethering). For my Android device, it’s just opening the Configuration, then More..., then Tethering & mobile Hotspot. Choose Setup mobile hotspot, give it a name (SSID), a password, choose WPA2 PSK for security and Save it. The hotspot can now be activated with a checkbox in Tethering & mobile Hotspot.
Find more help in these comprehensive guides for Android and IPhone.

Wireless Internet Connection
Setting up the wifi connection just requires changing the file wpa_supplicant.conf. If necessary, attach the USB wifi dongle, then boot the Raspberry Pi. Open wpa_supplicant.conf with

and change it to

but with your two letter country code instead of DE.
Enter the name of your wifi network for NETWORK and the network password for PASSWORD. Save and exit by pressing CTRL+x, then y.
Now, open /etc/network/interfaces with

and add

at the end of the file. Save and exit as like above, then reboot the Raspberry Pi with

Internet connection test
To test the connection, open a terminal and type

If the output is similar to

the internet connection is fine.