I assume that you are talking Internet here? and that your intentions are honourable
The basic method is to use a proxy. Steganos Internet Anonymiser is a fancy one that uses lists of proxies all around the world and changes them every minute or so.
Obviously you can be "seen" by your ISP, or you wouldn't be able to make contact with them.
To actually hide your identity you would have to find a wireless link and use that. You would then look like the owner of the link. There are free ones around depending on where you live, my local railway station for example. You have an IP but it would not be directly linked to you personally.