Casters get very easy to solo with later on. Sorcerers especially thanks to their fast cast and huge spellpoint pool. Indeed some of the raids have been soloed by sorcerers. I’ve soloed even end game quests I’d never done before(well end game back when the cap was 16, I haven’t played since they went micropay) with my poorly equipped and fairly badly built sorcerer.
Early on your best bet is avoiding enemies. Remember in DDO you rarely have to kill much of anything in a quest for completion. In the early game the sleep spell can be quite effective, though it peters off very,* very*, quickly due to the hd limitation on it. The various charm spells are excellent too and remain so throughout the game when soloing but can be kind of annoying for your team-mates later on unless you know what you are doing as you can charm enemies that need to die to complete the quest. Charm Person is available right off the bat and a sorcerer with that can solo pretty much all of kothos and the harbour with little difficulty on normal. And a skilled player who knows the quests can solo most of them through elite with out much trouble. Especially with hirelings.
The easiest way to solo for any character is, most of the time at least, to just run straight to the quest objective. Kill the boss/loot the quest objective/throw the lever that ends the quest or whatever else the quest is about and get out of there. Of course if you care about story you probably won’t want to do that. Sneaking is very doable for most quests though. Even as a mage. In fact especially as a mage since you have summon monster, invisibility, dimensional door, charm/dominate person/monster, hypnotic sphere and other such spells. And traps hurt monsters so if there’s a fire trap or something cast Resist Energy: Fire(or drink a potion/equip a robe in fact there’s a min lvl4 robe that has Fire Resist 20 on it that is usually dirt cheap in the auction house since its a very common drop it would be quite useful for a poorly equipped newbie) run around getting as many mobs following you as possible and drag them through the trap killing them all with out wasting spellpoints. Almost all traps are dodgeable as well so if you have good reflexes you can skip the Resist Energy or even use non elemental traps for this purpose.
Another good tip is that you can switch weapons, shields, robes, and accessories instantly. Even mages should carry a shield. If you are getting hit and just need to buy a few seconds for team-mates/traps/dots/summons/charms/hirelings/whathaveyou to kill what’s beating on you just swap to a shield and block(making sure to face the enemy, unlike most mmo’s that actually matters here!). It’s often much more effective, especially in groups, than running around like a loon as most mages do. But remember to swap the shield out before casting anything(or use a mithral light shield) to avoid a spell failure roll. If you can get your hands on a Robe of Invulnerability(ml:4) everything up to about lvl 8 will be a cakewalk. As the Damage Reduction 5/Magic is applicable to just about everything you’ll encounter other than incorporeal undead and some bosses until you reach the higher level quests.
Other than that the only tips I can think of are the obvious: be prepared. Never go anywhere(once you’re past lvl 3ish) without stacks of potions/wands/clickies of remove disease, remove poison, lesser restore, remove curse, all the protection from energies, for any melee character you’ll also want barkskin, haste, heroism, and maybe shield of faith until you get a good deflection bonus item and some way of applying resist energies for every element, except maybe sonic which is very rarely an issue. On my non casters I just collect five cloaks/rings of resist energy 10/20/30 depending on my level to swap out when needed. My casters all take the spell. And sometimes get the cloaks as well so I can still resist energy when around enemies who dispel a lot or just to save spell points when possible. In fact I usually try to have the most possible for my level fire and acid resists at pretty much all times no matter what.