How I did it:
Tanks and Healers: Non-stop dungeon spam, just queue in the highest available dungeon and speed run the hell out of it. This goes very quick, as back when I did it, both Tanks and Healers had insta queue's. This isn't very fun, but it's the quickest route to 80 and should take you more than a couple of hour per class.
The hardest part for Tanks and Healers is level 70 to 71, as HoH takes to long and the first ShB dungeon is 71.
I'd suggest to not use the dailies to level up Tanks and Healers, use those for the DPS.
DPS: Theoretically I'd assume using trusts is the quickest way. But it's a lot slower than than doing it with a real group. Personally I levelled a couple of DPS to 80 with trusts (to unlock their alternate outfits) and did all dailies every day (this should be +- 1.5 level a day), after all my trusts were 80 I made a PF and looked for like minded individuals.
If you can get a full party of people intend on dungeon rushing, you can get to 80 in a super fast rate.
Anyways: if you're playing the long game, just do all of your dailies each day and you'll get their in a month or two. If you want it faster, add some trust dungeons in the mix, if you want it really fast you need to look for like minded individuals.