After watching the video, they all look like regular 1 sec. crossfades to me. Am I missing something?

I wouldn't call the example you gave particularly smooth. Transitions are one of those highly subjective things. What one person may find pleasing, another may see as annoying, too fast or too slow. Probably the most common transition is a simple dissolve or crossfade. For sideshows all you need to do is drag the edge of one photo over the other. As you do you'll see a "x" start to appear on the timeline. The further you overlap, the longer it takes to transition.

If you want to go to something a little more fancy pick one of the presets from the transitions tab, drag it over the 'x' , let go, and then play back. Adjust the amount of overlap to adjust the length of time it takes to complete.

Linear wipes are nice. (image changes diagonally from a corner) somtimes a clockwipe works well. Don't be fooled by the probable rough appearance when previewing. That's due to all the pixels getting moved around. It will be "silky smooth" once you render. How smooth depends which transition you pick, if its appropriate for the images and the time span.

Edit:

If you just want to fade to/from black then grab a corner, watch for your cursor to change to a quarter circle and you'll see a double headed arrow. To fade in from black at the beginning of a image drag right, to fade to black at the end of a image drag the curved line that appears left as you hold down left mouse.