Tim,
The answer to your question will vary, depending on the solution you choose. If you're looking for a simple static HTML gallery, then you won't need anything special on the server side. For that, what you need to do is select the photos you want to export and do File->Export->To Folder. Then upload the contents of that folder to your server. It will create a nicely formatted set of pages suitable for showing off small galleries.
If you run the popular Gallery software (
http://gallery.menalto.com/), you can export to that too. However, this software requires additional configuration on the server side, which can be somewhat difficult. Once again, just select File->Export->To Gallery. You'll have to click "Add" to initially setup the information for the Gallery installation you've chosen.
If you're looking for a nice fast way to get your pictures online with some degree of interactivity, F-Spot can also export to the Picasaweb and Flickr services. You'll need to sign up for an account with those services first, then once again select "File->Export->To Flickr" (or picasaweb).
Finally, because of the open nature of F-Spot, everything is easily accessible from most programming languages. A few people, like myself, have gone all masochist and written our own custom interfaces that run on Web servers and access the F-Spot information directly. However, while many of these provide lots of flexibility, they're often difficult to get going.
--Patrick
