It's all Photoshop + After Effects. This is a tutorial I made a while back (originally for an exploitative site that I think people should avoid called "hitrecord"), explaining the basics of my animation process:

https://youtu.be/y2h0wLYe6PM

Some of it's out of date (especially the site-specific stuff) but those are the basics. I know a small handful of tricks that I use in different ways to create all sorts of animations. There are definitely better and more in-depth tutorials on YouTube that you can find to do just about anything you can imagine.

Photoshop Battles also has a tutorial page full of basics for picture editing, including After Effects:

https://www.reddit.com/r/photoshopbattles/wiki/tutorials