trying to track an ip address

If someone is using a hotmail account on the internet and they have been sending out emails, how can you track who is or who is not sending the email by an ip address. they could be using a computer in a hotel, a lap top with access to wireless internet outside commercial buildings. How does one define where an actual email comes from. and if the ip address goes back to a hotmail or yahoo address how can you find out who when you are all said and done. Does a hotmail or yahoo email account have it's own independent address over and above the internet service provider address?