One of the first decisions you'll need to make is what list software to use. There are several choices available, each with their own advantages and disadvantages. The deciding factor, however, should be "use whatever's easiest for you". If your ISP or workplace provides mailing list software, go with what's there.
If, however, you're in a position to make your own choice, here's a brief run-down of the pros and cons of various mailing list software.
Majordomo is probably the most common mailing list software around. It's easy for people to subscribe, fairly configurable (via email), and lots of people will be able to help you with it. On the down side, it doesn't do web archives without the help of 3rd-party tools like Hypermail or MHonArc, doesn't do moderation easily, and can overwhelm list owners with "bounce" and "approve" messages if subscribers' email addresses don't work. Majordomo is written in Perl, albeit nasty, messy, version 4 Perl which is pretty much impossible to work with. A new version is expected sometime "real soon now".
While the world waits for Majordomo's next version, Mailman is taking a lot of its market share. Mailman provides a web interface as the default means of subscribing to and administering lists, which is perfect for inexperienced list administrators. Email interfaces are also available, however. Mailman's great strengths include automatic web archives, mail-to-news gateways, very easy administration, excellent handling of "bounce" and "approval" messages, and simple mailing list moderation. On the down side, its email interface isn't as nice as Majordomo's, and not as many people know it.
Ezmlm is a mailing list manager designed to work with the QMail MTA. It is supposedly very fast and good at handling very high volume lists (hundreds or thousands of subscribers). On the down side, its email interface is pretty ugly.
LISTSERV is fairly common in Universities. It has a mail interface which is not too bad. Administration is usually fairly centralised, and you may need to get your site's postmaster to do a lot of the work for you. Generally speaking, don't use this unless it's your site's standard.
Lyris is a commercial list management system. I don't know much about it other than it has some web interfaces which look slick but are particularly unusable.
Free list hosting services are available at several places on the web. The advantage of these is that any schmuck can set up a list and run it. The disadvantage is that you'll usually get the host site's advertisements pasted into every email that goes to your list, and that the subscribers lists may be sold to commercial direct marketing organisations (read: SPAM mongers). Check whether the hosting site has a suitable privacy statement before inflicting a lifetime of junkmail on your list subscribers.