Open the Messages app
Open an existing conversation or start a new one
Tap the App Store icon or the Apps button next to the text field
Select #images or GIF search
Search for the GIF you want
Tap the GIF to insert it into the message
Tap the send button
If #images is not available, copy a GIF from Safari or another app
Paste the GIF into Messages and send it
You can also use a third-party keyboard or app that supports GIFs