This task has two stages: first, we identify and install firmware for the Wi-Fi adapter, and then we need to configure it for the wireless network.
We will try to identify the chipset of your Wi-Fi adapter (the part that handles the connection); this may not match the actual manufacturer of the device.
An approximate list of supported firmware can be found with this command:
sudo apt-cache search wireless firmware
This will produce results similar to the following output (disregarding any results without firmware in the package title):
atmel-firmware - Firmware for Atmel at76c50x wireless networking chips. firmware-atheros - Binary firmware for Atheros wireless cards firmware-brcm80211 - Binary firmware for Broadcom 802.11 ...