You could actually use those cheap earbuds they pack in for a smartphone. Same connector.
The consoles come with one. Sony packs in the earbud thing and MS a headset/mic combo. Both cheap but free is free if you don't care about quality. Though honestly I must say that using these is a bad experience for people on the other end. The microphones aren't that good so it's difficult at times to hear someone who is using them. You can spend anywhere up to hundreds for gaming headsets. So setting a max budget can allow you to get something of decent quality that will both allow you to hear things clearly and allow the people you're talking with to understand you.
For the most basic of gaming headsets I'd start with something from turtle beach. For $40 you get a pretty decent headset with a pretty ok microphone. It won't win any awards for sound quality but it works, and if you have the new XB1 controller with the 3.5mm port it works on that directly so you don't need an adapter to use it on both the PS4 and XB1. You can browse for other turtle beach models, they have stuff ranging from $15 to $200 or so. Alternatively if you have a headset designed for the PC with the microphone and audio cabled separated, you can buy an adapter to convert it into the single connector you need to go into the controller.
http://www.amazon.com/Turtle-Beach-...6174901&sr=8-12&keywords=turtle+beach+headset
Just make sure it has a connector like this if you want to plug it into the controller and not have to use a USB connection or anything like that. You'll only get stereo, some other headsets allow you to get positional audio/simulated surround.