It's a bit different without systemd, due to dependencies, but this guide should educate you on how to use the internet on a sysvinit Debian system.
Step one,
This can be done using
$ ip a
Interfaces look like enp2s0, wlp3s0, wls1 and so on.
Most ethernet interfaces start with "e", to connect to the internet, you just need to type one command:
# dhclient <interface>
Replace <interface> with your interface.
This implies you have an atheros card or have the firmware files downloaded, if not, read UPGRADING.md to find out how to enable non-free applications and download the firmware packages. (use DuckDuckGo)
Make sure your card isn't blocked, use rfkill for that one
$ man rfkill
for more info
Debian can't run NetworkManager without systemd, for WiFi, we'll use the interfaces file, located in /etc/network/interfaces.
Edit it, our editor now will be nano
# nano /etc/network/interfaces
In here, the file should look something like this:
# This file describes the network interfaces available on your system
# and how to activate them. For more information, see interfaces(5).
source /etc/network/interfaces.d/*
# The loopback network interface
auto lo
iface lo inet loopback
Add this to the file:
auto <interface>
iface <interface> inet dhcp
wpa-essid <ssid>
wpa-psk <password>
Replace:
<interface> with your interface
<ssid> with your ssid
<password> with the network's password
Save and quit it, reboot
# reboot
and you should be good to go.