The help center article is correct, the tricky part is finding the right link to paste in. The procedure for this is different for each site you post a gif from
Giphy has expanded their platform to support more media than just GIFs. If you're not copying the link to a GIF specifically, it will not convert properly here. The general rule is if the link ends in ".gif", it will properly embed within the post.
For example, if I copy a link to this Giphy clip, and paste it below:
https://giphy.com/clips/grinchmovie-grinch-illumination-movie-Y0NhkIdyT3TVBDWLkGit won't automatically embed, but if I copy a link to this GIF from Giphy:
https:\\media.giphy.com/media/v1.Y2lkPTc5MGI3NjExb2JhN2dkZ2RkazMxcDk0amx6MjBvaGV6bjVwdzgwYXA3cm80MXN2ZyZlcD12MV9pbnRlcm5hbF9naWZfYnlfaWQmY3Q9Zw/xUOrw4tlQfCTGmD5Kw/giphy.gif
(replacing // with \\ for demonstration)
On Giphy, when clicking the share button, if you see "Copy Clip Link" or anything else besides "Copy GIF Link" then the media you're trying to embed isn't a GIF, and won't convert properly.