Do I need a headset for the xbox 360 to talk to friends online?
In order to voice chat with other people via an Xbox 360, you need a headset or the Kinect accessory.
This Microsoft support article goes into specifics about what you need and how to get it set up.
Microsoft makes headsets, and so do a lot of third party manufacturers.
If you want your headset to also give you game audio, you'll have to buy one that has that specifically as a feature (like offerings from Turtle Beach or Astro Gaming). Most "Xbox 360 chat headsets" will not give you game audio as well as chat audio, as the jack on the controller is specifically designed with mono chat-only audio in mind.