I'm curious that lalimacefolle recommended trying octave harmonics first, this involves a lot of movement for the right hand, you may find it easier to practice with harmonics equivalent to those on the 3rd, 4th and 5th fret of open strings. If you have a wah pedal stick it on full treble and give yourself lots of gain. Try and keep relaxed with it, if you tense up you'll touch the strings with your right hand too hard or too long and will fail.
I find pinches easier with upstrokes, most guitarists find downstrokes easier. When you get the hang of scales with pinch harmonicswith either down or up strokes try learning to alternate pick up and downs, your right hand will move in figure of 8 shapes. Be prepared to suck, this takes lots of practice!
You may want to try some chords with pinches too. The easiest involve straight line movements for the pinching hand and I find upstrokes far easier 'cause it's hard not to mute the strings on down strokes with the fleshy base of your thumb.
The following involve straight up movements: 1st position minor shapes on the top 3 e.g 12,12,12), first position major on the next lowest (e.g. 12,12,12) and sus 4 shapes e.g (12,12,12) on lower strings. Diagonal shapes can also be used such as the root position minor shape on the EGB strings (e.g 5,6,7) root majors with the same shape on BGD and an augmented shape on lower sets of three.
One very cool trick is to play different harmonics from a single note, you will find that you can get a whole series of major triads like this. Try the following using your left hand (i.e. natural, non-pinched harmonics) just to see what I mean: 5,4,3 (frets used), now copy this with your right hand keeping your right hand the same distance from the bridge your left was from the nut.
You can keep moving closer and closer to the bridge getting higher and higher harmonics. It's possible to transpose a lick into another key by changing where you place your right hand on the strings!
One of my favourite tricks is to play one pinch harmonic, bend the note up and then play another pinch harmonic and bend it back down.
Anyway, enough from me, that should keep you going for a while.