A bit more info would be helpful. For example:
Which connector are you using?
What are you trying to display?
This is a good example of why you need to give as much info as possible to obtain help. There are any number of things that could be the problem.
1)The simplest is did you check to make sure the input for the hdmi port on the tv that you are attaching to is selected.
2)Have verified that hdmi port works properly by plugging another device that you know works into it?
3)Is this a genuine Apple adapter or a knock off?
4)Do the tv and iPod both work properly independent of each other? If yes, then will the setup work on another tv? If yes, it's the tv. If no it's the adapter.
This should be fairly easy to diagnose, so just eliminate all the possibilities.