What do you need? - Web Space
You will need an account with an Internet Service Provider that offers space to store your pages. Most ISPs include a basic amount of Web space in your subscription, so if you already have Internet access, you shouldn't have to spend more in order to publish your genealogy on the Web.
This basic Web space is typically at least 20Mb (megabyte), which is equivalent to about 20 million characters of text, but larger allocations increasingly common. Some providers even claim to offer "unlimited" Web space. If you are still to choose an ISP, make sure you get at least 20Mb.
If your ISP does not have Web space for subscribers, you should either change your provider or consider one of the services that offer free Web space.
If you just want to publish your family tree on the Web and no other material, then some genealogical software companies provide free Web space for customers to upload Web pages generated from their products. (See Genealogy Software.)
If your initial allocation is not enough for your needs, Internet providers will sell you additional Web space. This is mostly intended for business and professional users, and tends to be priced accordingly. If you are planning a Web site for a society or a group rather than for personal use, you will need to assess the total space needs and the probable cost. Of course, you can always rent more Web space as and when you need it, and in any case costs are falling all the time.
On the whole you are unlikely to need large amounts of space just for personal genealogy or for society and membership information. It's only if you wish to make indexes, transcripts or publications availableon-line, or high quality images, that you might need a larger allocation but even so, it will probably take a while to fill 20Mb. 
For a society Web site, or any site where you are offering data or imgaes that are likely to be popular, one thing to watch out for is not the limitation on space, but restrictions on bandwidth, i.e. the amount of data downloaded from your Web site. Most ISPs have a limit on this - so many Mb per month - and if you're going to have lots of visitors this limit may be exceeded. The ISP will then either close down access to your site temporarily or charge for the excess, which emans that it's important to look at this issue when setting up an account if you expect a high level of traffic on your site.
 Angelfire and Geocities are perhaps the best known of these, but there is an extensive list on Yahoo. Usually, your free Web space is "paid for" by carrying advertising, either in a banner on your page or in a floating window.
 To put this in perspective: the text of this on-line book takes up less than 500k (kilobytes), i.e. less than 3% of a 20Mb allocation. Even with the images, it takes less than 3Mb.