Extensions have now been added to the Apple Photo application with the release of El Capitan. At present(Jan 2016), there doesn't appear to be a huge number of tools available but I guess they will start to appear over time. Affinity Photo have jumped in with their own set of 6 useful tools that sort of match (to a lesser extant) the tools in the application such as develop and Liquify. So how to get them to appear in the first place ???
Well, they are added by the app in the first place and if you have no extensions, then either the app doesn't add them or something has failed in the extension install process and in the case of Affinity Photo, I would contacting them with the details as they should be available if you are using 1.4+. OK, first thing to do is to go to the Apple Photo or to the system preferences, either is fine. In system preferences, go to the extensions and you will see an entry for photos, click on that on the left side panel and you will see 6 (or more if you have other extensions installed) and you can select them or not depending on if you wish to add them to the Apple Photo app. Assuming that you have selected them all. You can also do the same in the Apple Photo app via the extensions button at the bottom of the edit panel.
Start up Apple Photo and then click on a picture though before you do anything, I would suggest that you duplicate the photo and at least you can always go back to the source image. Far right at the top there is a little edit button (could they have made it any more obscure ?? why isn't the edit in the edit menu ?? ) Anyway, once you are in edit mode, you will see the picture and the tools / extensions / filters etc down the right side (enhance, rotate, crop, filters, adjust, retouch, red-eye, extensions). Click the extensions and if the installed items are there (excellent) if not then go for the more and then add them via the preferences. Now you should have all the extensions to play with in the application.
There are a number (six) such as develop, haze, liquify, miniature, etc. They work in much the same way as the tools with Affinity Photo so if you want to tweak the exposure etc then you can use the develop tool and if you want to warp the image in 1000s of ways, you can use the liquify. I would love to see the "Affinity Photo Mirror Extension". Hopefully more will be released with the 1.5 release ?? Anyway, once you have done all your edits, you can click the cancel or save changes. An error message appears with my extensions in some cases (perhaps that is just my setup). You can then revert to original or you click done.
You can find out more via our video tutorial