Here's an easy way to get that sound, it was one of the first tricks I learned years back. Lightly pace your finger over the 9th fret on the top 2 strings, pick the notes and let the two notes ring out. If you don't know what I mean, it is the same pricipal as ringing out the harmonics when you tune the strings using 5th to 7th fret on alternate strings.
Now, to get the Dime sound you need to have decent pickups and a good distortion setting that allows lets you get a long sustain. Pick the harmonic on the top two strings at the 9th fret then do a dive bomb with your trem (also an essential part of equipment in the technique).
Experiment along the fretboard and you will find some great harmonics. The best are at 3, 5, 7, 9, 12 and so on up the next 12 frets.
A nice dive bomb can be got by ringing an open high E (top string), then as the note rings out, ever so lightly place your finger over a harmonic as you dive the trem forward. Gives a great sound going from an open clean note up several tones to the sqeel as it dive down and the strings rattle off the pickups.
You can also drop the trem forward a bit and dive back wards or as Dime did a lot, turn the trem arm the opposite way so it faces away from the strings, hit a high 17th fret harmonic then lean on the arm as far back as you can go. Make sure you have good strings and a well locaked trem otherwise the strings will break and/or the whoe set up will go out of tune. Also, use your ear to judgte how far to dive back or forward if you want to keep in key with the rest of the licks in the solo.
Good luck!