While you can use either mobile or web, it's much simpler to find your desired URI from the web version of Spotify.
Click the three stacked dots to the right of the music track name.
The track URI should look like this:
Click the album.
Copy Spotify URI that appears in address bar of Spotify web version.
Click the three dots next to the heart icon.
Choose Share > Copy Album Link
The album URL should look like this:
Visit the playlist you want to share.
Select the three dots next to the heart icon.
Select Share > Copy Playlist Link
Your URI should be in the following format:
Click the three dots below the artist name.
Select Share to open the share menu.
Copy Artist Link
Keep in mind that the artist profile and user profile are not the same thing. The URL of an artist profile will include the artist name.
The artist URL should be in the following format:
Visit the User profile and copy the Spotify URI that appears in the address bar.
The User URL should be in the following format:
Note: A User profile is not the same thing as an Artist profile.