To play harmonic on the ukulele begin on the 12th fret.
Press gently on the string over the 12th as you pick it. The "pressing" action is really a touch of the string, hence the gentle press.
This can be done for all stings on the 12th fret as well as the 7th fret and 5th fret.
The ukulele harmonics give off a chim-like sound, which can be combined with any song to significantly enhance it... or potentially you can play an entire song using harmoics, my favourite is silent night because it helps to make it sound ever so peaceful...
Hope this is useful to you aspirirng ukeists out there.