Hello Sophie,
Congratulations on your new Apple TV! Also, thank you for the question. It sounds like you are trying to play videos or music from your iOS device. Instead of using Home Sharing for this, you would use AirPlay.
Use the steps in the following article to AirPlay music, photos, and video wirelessly to your Apple TV:
iOS: Use AirPlay to wirelessly stream content
http://support.apple.com/kb/ht4437
If you would like the entire screen of your iOS device to appear on your television, you can using AirPlay Mirroring. Use the steps in this article:
iOS: Use AirPlay Mirroring
http://support.apple.com/kb/ht5209
Thank you for using Apple Support Communities.
Best,
Sheila M.