iWeb itself still works just as before.
MobileMe, which provided website hosting, is closed; and iCloud does not provide website hosting. However this does not affect iWeb. You can still make websites and upload them to another hosting service - there are plenty to choose from.
Up to and including iWeb '08, it was only possible to publish to other hosts by 'Publishing to a folder' and then uploading that local folder to a website host using a separate FTP client. From iWeb '09 an FTP method was built-in, making it easier to publish to a host other than MobileMe. So the exact method you will use depends on which version of iWeb you have.
There are a few minor functions in iWeb which were dependent on MobileMe and will not work elsewhere, including hits counter and blog comments.
More details here: