Posting anonymously to a mailing list can be useful if the topic of discussion might be considered embarassing to the poster. It is much better to post anonymously than to go without the help you may need.
The easiest way to post anonymously is to get a free e-mail address different than your normal account. Yahoo maintains a list of these kind of providers here. Of these, Yahoo! Mail, HotMail and Juno work pretty well in my personal experience. If you don't mind reading your mail in a web browser, there are lots of additional choices such as hotmail. The "Free Forwarding" section can also be used for this, although it is a little harder to set up. When you sign up for the free e-mail account, there is often an ability to "look you up" on their web page. Make sure you don't select that option if you want to maintain anonymity.
Once you have a free anonymous e-mail account, you have to configure your e-mail client to use it. Eudora has a nice personality feature that I use for this purpose. (I don't know if the free version has this.) In any case, if you set up your return address to be your regular address, then you have given your true identity away. If you are unsure, the safest thing would be to set up a different e-mail program for reading from those lists on which you would like to maintain anonymity. For example, installing Eudora into a different directory. Then set up your return address and name, etc. to the alternate name you have chosen to appear as on those lists.
If you are in the habit of signing your name on e-mail, you'll have to be careful not to put your real name in the e-mail. The best way around that is to set up Signatures on each of your e-mail programs that keep you from manually signing everything.
On closed mailing lists, if you accidentally post from your real account, your e-mail will bounce back. Encourage your mail list provider to close the list so that only members of the list can post. This will help ensure your privacy.
Finally, lists that provide for anonymous posting should not provide archives in order to insure privacy. If your real name gets out somehow, then people can't easily go back through the archive and read all about you.