There are a number of ways of testing if 90DNS is working properly:
You can use the
90DNS Tester, a Windows application. It'll check if 90DNS can be used in your connection (sometimes your ISP hijacks DNS).
You can also use the
Switch 90DNS Tester, a homebrew for your Switch (it doens't work on the latest system updates, though).
You can also setup 90DNS as the default DNS for your router/PC and test by entering
90dns.test on your preferred browser. It'll notify you if 90DNS it's working - it it's not, it'll simply not load the page.
If you want to be extra safe, you should setup Atmosphère DNS.mitm service. To do so, read
this. It'll block Nintendo's telemetry regardless if 90DNS is active or not.