Hi Jack
I would expect the NAS to get its IP address from your LAN's router, using DHCP. Your router may have a web interface that shows the devices on the LAN that have obtained IP address leases, and it will show their MAC addresses. You can search the internet for the first 3 parts of the MAC address to find the manufacturer. Such a search would most likely show D-Link, confirming that it's the correct device, and the corresponding IP address can be used to connect.
As Bodzio suggested, you could scan your network (eg with "Fing" for Android or "Advanced IP Scanner" for Windows) to see what devices are there. The one that's new is going to be the NAS. These types of tools can sometimes indicate the manufacturer.
Another thing to try is the vendor firmware's default IP address, which is 192.168.0.32. If your LAN has a different network address, you might need to temporarily change the IP address of a laptop to use the same subnet, with a different IP address such as 192.168.0.33. Once the laptop and the NAS are on the same subnet, you should be able to ping the IP address from a command line, or connect to the IP address using a browser.
Below are generic instructions that I follow, if I have any device that appears to be running but where I don't know its IP address:
If you have a Windows PC/laptop, install and run Wireshark, then try plugging it directly into the device's ethernet port (from the laptop's ethernet to the device's ethernet). Wireshark will show any traffic sent from the device, and will give clues as to its network status. This might include DHCP "discover" packets, in which case, the device is trying to get an IP address from the LAN router. Or you might see ARP requests from a specific IP address, in which case, the device is trying to reach out to something using its pre-configured IP address, which you can then copy down, and use it to connect. If this indicates that the device has an IP address that is not in the same subnet as your LAN, then you can temporarily reconfigure your laptop to be on the same subnet as the device (but with a different IP address), and then connect to it from your laptop. Once you've connected, you can login to the management interface and assign a static IP address from the correct subnet and reboot.
Cheers
Jeremy