Have a look on this site at the River Don page
http://fishingthefly.co.uk/river-don-brown-trout-fishing.html loads of choices there.
I can only comment on a few beats but will try to help:
ADAA beats. ADAA have some excellent fishing on the lower to middle beats of the Don upto around Kintore. The ADAA website has excellent advice and beat summaries, well worth a read.
Monymusk. Possibly one of the most famous beats on the Don, split into 13 beats over 10 miles of water.
http://www.monymusk.com/index.asp?sec=5 Famed for big trout, but it can be a bit moody, especially with an easterly wind. Worth going to the Grant Arms and having a look through the catch reports. I was there a few weeks back abd has a fish of around 5 pounds, but when I entered it into the book, the guy before had had a 7.5 pounder! Some lovely "proper" pools as well as long glides.
Candacraig/Edinglassie/Tornashean. All three beats are available on the same ticket now. Some beautiful upper Don fishing in stunning sceanary. £20 gives access to 10.5 miles of double bank. Up there a few weeks back and we had the entire 10.5 miles to ourselves. All sorts of water from deep, dark pools to shallow riffles with just about everything else in between. Plenty of fish showing including a few salmon.
I think the best advice is to join the ADAA as that will give you access on the lower Don and also parts of the Ythan, both within 20 minutes of your door step. As for advice on tactics etc, I will leave that to those who are better anglers than me, but I have caught on swung wet flies, up and down stream dries, Czech and standard nymphs and streamers. There is water for every tactic available so go fill ya boots.