The Pacifist Challenge is a popular challenge of gameplay where one must level a character in very unusual circumstances. This challenge is not regulated as much as the Ironman Challenge and the only rule is no killing.
The most important thing to remember is this is a self-challenge, not a competition.
- No killing (not even critters)
- No grouping with other characters just for experience, their kills count against you.
As a rule, even very first quest requires killing. Hence the pacifist abandons the usual game flow and needs to think that else could be done. One of the first approaches may be to explore the territory. Discovering a new area gives more or less same amount of points as killing a mob. It is important to learn to avoiding mobs and evading from the battle. Normally you cannot just run away from the mob in combat, but applying something like early available may help to evade. Running towards guards to seek protection may be acceptable, if the mob just runs away after seeing them. For the 1-10 level characters and mobs in front of the level 80 guards, this is often the case. Later in the game, there are some means of fighting that do not kill (traps, etc). They may be useful even for a pacifist.
You may also decide that destroying something that is not alive is not killing. For instance, mechanical mobs are very obviously machines (elementals are somewhat more questionable). Of course, thinking only makes sense if you play on your own. If you join the pacifist community, you must follow the rules of that community - often even destroying the ice sculpture may count as kill, because this increments the kill count as visible via WOW API.
There are also many quests that require to find or collect something. However somebody who never killed may not be entitled to take such quests. For instance, if the Blood Elf refuses to kill these Mana Wyrms (the first quest to do), there are no other task even after reaching the level 3 via alternative means. If quests are not accessible, it may be possible to raise some money by selling the own gear and clothes.
Finally, since professions become available (level 5 required), it is possible to learn a gathering profession and travel around by just collecting resources. From this point the progress may become more sustainable, even if many resources may be much more difficult to approach if you cannot fight with the mobs nearby.
While there is no strict rule "never be killed" with this playing approach, using death as a way to achieve something (evade, for instance) degrades the game into comedy, so may be better to think how to get without this.
If you want to be listed in some "pacifist community website", beware of the possible additional rules (no own death, no buffs, etc.)