few things..
make sure your action is as low as possible. Take it to a pro if needed to get the neck straight, frets dressed, etc. Once that is all set...
Check this out. Most of us fret a lot harder than we need to. Pick a fret, any fret, and pick a harmonic there. Now, slowly apply more pressure until the note develops. See how little pressure it actually takes to make a note sound? Not much at all.
I would recommend lightening up on your picking hand as well. Some would argue, but I believe that while you're learning how to do this, its very difficult to be tense in one arm and relaxed in the other. Just relax in general. Remember, you're not doing vector calculus, and you're not lifting weights. You're playing music. Lighten up.
Hope this helps. Soon you'll be playing circles around the guitar player

The speed that comes with playing light is amazing.