Hello Daphne, other than apps, emojis are usually bundled with special keyboard software. That means you should be able to find them right where they should be, or rather right where you can input them anyway -- on the on-screen keyboard.
So to find any emojis that are already on your ZTE Majesty, if there are really any of them there at all, just fire up the messaging app and use the on-screen keyboard. Try looking for a button that might show you all the emojis that are available for use.
In case you can't find it, don't worry. You can just download emoji keyboards to get started. Go to Google Play and search for emoji keyboard then download whichever one that you like so you can try it. Go ahead and try the above tips to see what works. Hope this answered your question!