The easiest is online services, of which there are two main ones ... FlickrSlidr and PictoBrowser. Both generate code which you can simply copy and paste into your website HTML.
FlickrSlidr is the easiest and has some basic configuration options. However its limitations is in end users browsing pictures.
PictoBrowser is more of a traditional gallery and also supports Picasa, however the builder uses Flash and although the interface looks simple it is in fact clunky and just about crashed my PC.
However there is a simple way, using a direct Flickr API and iFrames using a piece of code supplied on this site. The code can also be made to be standards compliant.
I'm not sure about slideshows though, and I'd prefer to randomise static Flickr images. There are plugins available to do that too.
Interested to hear any other ways people have been able to achieve it.