Based on your configuration, things may vary
1. Arduino connected to local area network.
In here to reach the Arduino, you will have to do this
- Configure your cell phone or whatever device is sending data to the Arduino, to push packets to your internet external IP address and to a specific port ( as an example use port 5000 )
- Configure the Arduino with a static IP address on your local area network ( as en example: 192.168.0.10)
- Configure your router to forward port (5000) to the Arduino fixed IP Address ( 192.168.0.10 )
- make sure the port is not blocked by the router firewall.
Your system will work no different than on a local network
2. Arduino is connected to the internet directly using the cell modem and if the SIM is M2M, you will need a middleware or at least a known configuration. Also in this case, you need to know that many operators limit the incoming traffic (meaning how long the listening port stays active after the last message sent by the device).