If you are trying to use this USB adapter to connect your 2011.12 Raspberry Pi to connect to WiFi you may have difficulty because there is not driver preinstalled for it from the version of Linux installed using the Raspberry Pi Imager. What you will need is the rtl8188eu driver. The following instructions will get your Pi up and running on WiFi.
To check which USB adapter you have, run lsusb
and see if it is an adapter from Realtek Semiconductor Corp. If it matches the name above the instructions below will help you build and install the required driver.
First, install the dependencies.
sudo apt update
sudo apt-get install -f
sudo apt-get dist-upgrade
sudo apt-get -y install dkms build-essential git
Next, build and install the driver, then reboot.
git clone https://github.com/lwfinger/rtl8188eu.git
cd rtl8188eu
make
sudo make install
sudo reboot
Give it a moment to boot up and get an IP via DHCP and you will be able to SSH into your account.
Verify the driver is installed with this command.
lsmod | grep -iE 'rtl|8188eu'