There are 3 ways you can easily find your Synology NAS on your network
Synology Web Assistant
This is a quick and very easy way from your computer to find your Synology DSM.
Once found, click on Connect and then you can login with your Username and Password
Synology Assistant Software
You will need to go to the Synology Download Center website and then choose your Synology type and model which will then redirect you to Utilities page where you can then download the Synology Assistant for your computer. It is compatible with Windows, Mac, Fedora and Ubuntu.
Once installed, open Synology Assistant and under the management tab, click search which will then locate your device and lastly click connect
DS Finder Apple & Android App
If you have an Android or Apple device that supports Apps, then this is a very simple way to locate and access the Synology DSM