To find your Spotify URI, just head to your Spotify Artist Profile and click the 3 dots next to your artist name.
From here, you can click Share and Copy link to artist. This'll give you a long link like the image below. Your Spotify URI will be made up of spotify:artist: and the numbers shown.
For example, spotify:artist:4rDcfb3TEWyx0BKdzKG24I is the Spotify URI for this specific artist link.
If you need any help finding your music's Spotify URI or a URI of a song which isn't released yet, give us an email at firstname.lastname@example.org and we'll help you out. 🤝
There's more info about Spotify URIs here.