Download the sound. Tap Download on the sound you want. On iPhone it saves to the Downloads folder in the Files app.
Open it in Files. Open the Files app, go to Downloads, and tap the sound to preview it.
Share → Use as Ringtone. Tap the Share button, scroll (tap More if needed) and choose Use as Ringtone. iOS opens Settings with the new sound selected.
Use it for alerts too. In Settings → Sounds & Haptics you can pick the same sound for Text Tone, Calendar Alerts or Reminder Alerts, or assign it to one contact.
On iOS 18 or earlier: import the file into GarageBand on your iPhone (Loops → Files → Browse items from the Files app), drag it onto a track, then in My Songs press and hold the project → Share → Ringtone → Export. On a Mac: connect your iPhone, select it in the Finder sidebar, and drag the .m4r file onto its window.