It would be hard to find a class that solos as easily as a necro, shamans are no exception.
Shamans are just not as efficient as necros and with the absence of a pet early you're forced to either root/rot or melée/dot/nuke (I prefer the latter). Once you get canni and regen you'll get close to necro regen but with a lot more button mashing.
It's amazing how many group invites you get as a shaman if you leave /anon or /role off. Even if you're not in the same zone. Groups actively look for em. It's nice
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My basic tactic as a 16 shaman is to throw on a slow as opener (if mob is close to my level), disease dot, poison dot and melée. If by the time the poison dot wears off the mob is not close to dead/walking I'll fire off spirit strike, which is a surprisingly good nuke at the level we get it. I try to time it so my nuke sends it to about 15% hp and is on it's deathmarch.