[Unit]
Description=node-web

[Service]
ExecStart=/usr/bin/node /home/noded/node-web/index.js
Restart=always
#StandardOutput=syslog
#StandardError=syslog
SyslogIdentifier=node-web
User=noded
Group=noded
Environment=NODE_ENV=production
WorkingDirectory=/home/noded/node-web/

[Install]
WantedBy=multi-user.target

Copy your service file into the /etc/systemd/system/.service

Reload service files (systemctl daemon-reload)
Start it with systemctl start node-web.

Enable it to run on boot with systemctl enable node-web.

See logs with journalctl -u node-web