Well, there is no any kind of secrets.
1. Navigate to your profile settings -> browsing settings
2. Be sure to check "Unoptimized" format.
Jpeg are the same file format as jpg, some people don't know about it
3. Find any post you want to get image from. Or image itself.
4. Click RMB on the image -> save image as...
Success! You're great.
In addition to the setting TD mentioned, I'd like to point out that there is a "width=###" parameter in each image's url which controls its size (eg https://image.civitai.com/xG1nkqKTMzGDvpLrqFT7WA/0ca08e56-e2f1-4df1-8f30-19d70836c380/width=640/n3.jpeg). Due to the variation, I assume it corresponds to the source image's, but it can technically be increased beyond the default (or decreased), so there isn't a "max resolution" per se - the site can increase it on request. It's not recommended to go beyond ~1000 though, takes a long time to load (and strains the server probably).
Note that the API returns all images with fixed width=450, one needs to increase that to a reasonable value themselves, unfortunately.