Open the GIF in Safari, Messages, Mail, or Photos
Press and hold the GIF
Tap Save Image
Open the Photos app
Find the GIF in Recents or Animated
If needed, use the Files app to save the GIF from email or browser downloads
If the GIF is in Messages, tap and hold it, then tap Save
If the GIF does not animate in Photos, make sure it was saved as a .gif file and not converted to a still image