Every class is good at soloing, and shaman are no exception. We can do it pretty darn well.
As to strategy, you should always have your weapon buff on. Lightning shield isn't very useful in groups, but soling it's GOLD. Our most efficient damage spell by far, and you can cast it before, between, or during fights. If I'm trying to mow through monsters, I pull with a lightning bolt, maybe another while he runs, follow with flame shock as they close with me, then melee. Keep flame shock DOT and lightning shield up. Don't try to heal during fights unless you're going to lose, try to heal between fights. If the enemy tries to run, frost shock to finish. All of that is if you're just trying to kill monsters quickly; it's not very efficient. When farming lower-level enemies, you're better off not using any damage spells. Just drop stoneskin totem, drop searing totem, and melee with a buffed weapon. You'll kill more slowly, but you'll rarely have to sit and drink.
For any dangerous fight, you should be dropping totems in addition to Lightning Shield and Flame Shock casts. Stoneskin is lovely, lovely, lovely for long fights or fights vs multiple opponents; if you even think you'll get an add stoneskin is gold. Searing Totem is VERY mana-efficient if you can get it to last its full duration, and is a good supplement to a long fight. Healing Stream totem is along the same lines: overkill for quick fights, very efficient for long ones.
Some shaman pick up the two-handed weapons talent. I believe this talent is more useful in groups. I know that whenever I used a two-handed weapon soloing I sorely missed the huge armor boost that comes from a shield. However, it's hard to argue with the damage a two-hander brings. For soloing, you're better off with a shield because you're your own tank, but in groups, grab the two-hander for the extra DPS.
Enemy casters are a special case. For them, Earth Shock and Grounding Totem are HUGE advantages for a shaman. Earth Shock is the second attack spell you learn, and while it's not very mana efficient it's front-loaded (deals its damage in one burst, as opposed to Flame Shock). After you start getting more shocks, you should probably use a less-powerful version of Earth Shock to save mana, since you only care about the interrupt anyway. Earth Shock interrupts enemy casters and prevents them from casting for two seconds. This is a huge advantage. Earth Shock also works on certain non-magic monsters whose abilities have a cast time. An example would be the spitting spiders in Stonetalon. Those guys don't use mana, but they have a nasty venom spit attack. BUT, you can interrupt the attack with Earth Shock. Wonderful, wonderful ability. Grounding totem is another key ability. Currently it's bugged, but it's useful even so.
"The devil's greatest trick is to convince us that he does not exist."
Evil is real. Aku soku zan.