A MIDI controller is an USB device you plug on your computer. Most of them also contains a soundcard to plug headphones.
Headphone splitter cables
If you only have one stereo output (no midi controller), you need a special cable which splits the stereo signal to plug headphones.
If you want to step up your DJ game and style, you will need good headphones. Here are the most popular ones.
DJ audio interfaces
If you don't have a midi controller and might need a DJ soundcard which with 2 stereo outputs for plugging headphones.
DJ audio mixers
Here is a selecting of DJ audio mixers. It is like controllers but only for the mixer part (eq, volume faders, crossfader...).
Here a selection of MIDI launchpads. These device are like an instrument which allow to create music live.
Nothing can match the feeling and the style of mixing with vinyls. Scratching on vinyl is just the best DJ experience ever.
You will need some loud speakers for your next party or simply to blast the ears of your neighbors :)
You will need some crazy lights to turn your room into a nightclub! They are pretty cheap too.