There are a few ways of doing this. Firstly I'll assume you're using Photoshop.
1. Make sure the part of the image you want is selected.
2. Click on the arrow on the side of the paths palette in Photoshop and select 'Make work Path'
2. Next select the same menu and select 'Save Path'
3. Go to the File menu and select Export>Export Paths to Illustrator
4. select the path you have saved and save it to where ever you like.
Illustrator
Now once you've opened the file in Illustrator you'll just see a blank page with some crops marks indicating the overall shape of the path.
To delete the crop marks -
1. select all
2. Select the Object menu then Crop Area>Release
4. Delete the newly highlighted square
5. Selecting all again will highlight the path you have exported for you to do with what ever you like
It's worth messing around with the tolerance setting in Photoshop a bit or you will end up with a path consisting of thousands of point.
Hope this helps, it is easier than it looks
