Configuring an IP connection on your watch has to be done manually until a GUI settings option is available. On watches that support WLAN, you can enable Wi-Fi and configure the connection using connmanctl like described below. Forwarding IP requests to a connected PC via USB is another option, explained in the second paragraph.

By default, there is no root or ceres password, and no firewall rules. A password can be set using the passwd command.

IP over WLAN

Connect to your watch using ssh root@ or adb shell.

# connmanctl
connmanctl> enable wifi
connmanctl> scan wifi
connmanctl> services
connmanctl> agent on
connmanctl> connect wifi_CODE-FOR-YOUR-SSID
connmanctl> quit

Check whether an IP address has been assigned to the watch using ip a show dev wlan0 or ifconfig wlan0.

Note that activated WLAN consumes additional power. Currently, it is recommended to disable the function after use. connmanctl disable wifi is used to disable Wi-Fi and power off WLAN temporarily. connmanctl enable wifi activates WLAN again and connects to the last used Wi-Fi network.

Some more details on ArchWiki

IP over USB

Configure a NAT on your computer (Note: Replace eth0 with the name of the interface that connects your computer to the Internet) with:

echo 1 > /proc/sys/net/ipv4/ip_forward
iptables -t nat -A POSTROUTING -o eth0 -j MASQUERADE

Configure a default gateway and DNS on the watch with the following commands ran via SSH:

route add default gw
echo "nameserver" >> /etc/resolv.conf