its not done with the plucking hand, with that you just pluck as normal.
its all to do with the fretting hand. Its kinda tricky at first but try it on the 12th fret (there are other certain frets that harmonics occur on, google for these). You have to sort of rest your finger on the string so that if you don't lift it you get a numb. DO NOT PRESS DOWN!
To get the harmonic just lift your finger sharply off the string whilst at the same time you play that string. Hopefully you'll get a harmonic (btw guitar needs to be tuned correctly!)
2005 Martin DX1R Dreadnought, 1994 Fender USA Lonestar Stratocaster, 2005 Gibson Firebird Studio, Aria Acoustic 4String Bass, 25W Fender Champion 110, 100W Peavey Linebacker Bass Amp, Crap Amp, Lots of Boss Pedals