The Witch Doctor is in a sense the most basic class available in Diablo III. Harkening back to the ‘olden days’ of Diablo II, the Witch Doctor runs off of a Mana pool that refills over time, and only three skills in the entire set available to the class do not consume mana- all three of which are on set timers.
In a certain sense, the Witch Doctor is comparable to the Diablo II Necromancer- relying on a combination of mostly Poison damage and summon-type effects, but with enough other abilities that those two main tendencies can actually be totally sidestepped.
One of the more interesting traits of the Witch Doctor is that, unlike any of the other classes in Diablo III, it completely lacks any form of self-defense skill- while a number of its skills will manipulate the battlefield, it has nothing to reduce incoming damage in a more direct manner. This means that you will need to be very careful about any time you spend in melee range of anything- despite the short range of some of the Witch Doctor’s skills, you simply cannot stand close to things for very long at all.
On the upside, the summon skills take little to no management, and the vast majority of the Witch Doctor’s skills are useful at a good distance- many of them will reach across the whole screen.
Unlike the Monk, Demon Hunter, or Barbarian, the Witch Doctor lacks any direct method of generating its resource, and unlike the Wizard, it doesn’t have any frequent-use skills that innately don’t rely on that resource either. Because of this, it is very easy to run out of Mana, particularly in a difficult situation. You should always be ready to abandon a fight for a few seconds so you can generate more mana, and keep yourself focused more on maintaining a steady level of activity than on blowing out your mana as fast as possible. This isn’t so say that a Witch Doctor can’t ‘alpha strike’ and burn out everything they’ve got in a frontloaded blast of damage, but doing so is far more hazardous, as it leaves you unable to do anything at all for a time afterwards.
On the other hand, the mana pool for a Witch Doctor is immense compared even to the Demon Hunter’s Hatred or the Monk’s Discipline pool, so be aware that the large numbers attached to the Mana cost of many skills aren’t as daunting as they would be with a typical resource pool. This is particularly so given that the Witch Doctor’s Mana pool grows as the Witch Doctor’s level increases, meaning that once-prohibitive costs can actually become fairly reasonable and passable Mana costs quickly become negligibly small.
The Witch Doctor loves a good opportunity to stand still, so finding a relatively safe vantage point for any battle will always be to your advantage. Similarly, try not to draw too much attention with direct-fire damage skills, unless you’re heavily invested in battlefield control effects- and even then it’s better not to get things to attack you.
Bear in mind as well that the Witch Doctor and Wizard have similar requirements from their gear- moreso than the Monk and Demon Hunter with each other- and so in theory you could pass on gear from one class to the other pretty easily.