Soloing instances as a hunter generally involves less "AOE everything" technique. Instead, you perform managed pulls of small numbers of mobs -- 3-4, though you can go larger if you're talking low level instances -- and single target kill the target your pet is attacking.
Some tenacity pets -- specifically, the Bear and Crocolisk famlies -- have better multi-target threat special skills. The Bear family has a multi-target swipe, which allows them to build up threat, and the Crocolisk family has a Bad Attidue special with 40% uptime, allowing a counter-attack for all attacks on the Crocolisk.
Using Misdirect (obtained at level 70), it is possible to redirect threat to the pet for up to three attacks. This allows you to use a multi-shot (or other threat generating attacks) to keep threat on your pet. With Feign Death being a 100% threat dump, it is also possible to drop threat when needed more effectively than many other pet classes.
For really low level instances, it should be possible to gather up large numbers of mobs with a pet, and AoE them down with volley or similar: no class will have any serious amount of trouble quickly soloing the Stockades, I don't think.
In 3.3, Misdirect is being changed to redirect all threat for four seconds to the pet, rather than being limited to three damaging attacks. This means that after 3.3 is released, you will be able to gather up a large set of mobs, misdirect to your pet, and use volley to generate a significant amount of threat, quickly. The benefits of this for soloing are obvious: you should be able to complete almost a full volley giving your pet the threat, and complete another volley to finish off most low level instance packs.
Until then -- and possibly after as well -- the best technique is likely going to continue to be to gather small packs, single target kill them, and move on to the next ones. Tossing in some AOE to finish off low-health targets shouldn't be a significant problem, nor will using multi-shot to do additional damage while hitting your primary target. However, it is unlikely you will be pulling an entire instance, and then just dropping an AoE to kill all the mobs like you can with some plate wearing strong-AoE classes.
Generally speaking, for soloing as a hunter, you will want:
A pull will typically start with Misdirect, then waiting a few seconds to let the cooldown get closer to being up. Hit Mend Pet, then send pet in, and pop Bestial Wrath immediately before your pet's Thunderstomp. (Previously, this was specific to Gorillas; now, available to all Tenacity pets.) Multi-shot (with multiple targets) or Multi->Arcane->Steady if a single target. This will give your pet a significant aggro lead. Pop Misdirect again as soon as it's up, and remember to use high-threat generating abilities like Arcane/Multi shot when doing so, rather than using up serpent sting ticks where possible.
You can then start a typical DPS rotation, remembering to keep mend pet up as necessary.
Overall, hunters are able to solo a significant amount of content with good pet management, using the single target, rather than AoE, style of killing enemies.