Bone Necromancer Starting Guide (Levels 1 - 30)

Most Important Stats: Faster Cast Rate (FCR) (48% at this point in the game would be fantastic), Strength to wear a larger belt & Energy for more Mana - rest into Vitality
Starting Tips: This build is heavily dependent on Potions and you're going to need to constantly restock your inventory and Potion belt to look like my screenshot above.
Good Early Gear: Stealth Rune Word and Rhyme Rune Word in a Shrunken Head with +Skills. +Teeth Wands or Shrunken Heads; check Akara in Rogue Encampment for a +Teeth Wand. Any Rings/Amulets/Wands/Gear with FCR on it.

Note: You can also start out as a Summon Necromancer instead of a Bone Necromancer. This is regarded as one of the most boring builds in the game though especially early on so I went with Bonemancer instead.

Talent Point Allocation:

1 Clay Golem
1 Golem Mastery (Only really useful with +Skills)
1 Summon Resist (Only really useful with +Skills)
1 Bone Armor
(+) 1 Bone Wall
(+) 4 Bone Prison
1 Amplify Damage
1 Iron Maiden (Required for Duriel & other Normal bosses)
1 Corpse Explosion
(+) 12 Teeth
(+) 8 Bone Spear
(+) = Good spot to place additional Skill Points

Poison and Bone is the strongest spec you can do on a Necromancer for the first 30 levels and it also is the highest DPS Necromancer spec in the entire game. Until level 18 your main ability is going to be Teeth; you'll want to purchase Bone Spear immediately when you are able to and you'll be using this for single target DPS over Teeth. When fighting large packs of enemies Teeth will still be good until Act 4 and 5 when it really starts to fall off.

Clay Golem is recommended to get immediately at level 6 when you can as he'll be your tank. Amplify Damage is a pre-req for Iron Maiden which is a curse that you'll pretty much only be using on bosses like Duriel, Mephisto, Diablo and Baal. With this ability you can easily defeat all of these bosses with the "quit hitting yourself" method.

Teeth is an interesting ability since the position of your cursor affects how it works. Use my two screenshots below to see what I mean; when your cursor is close to your character Teeth has a very wide spread, almost like a frontal nova. When your cursor is further away from your character then Teeth's spread is much more clustered together like a wave in front of you.

Bone Spear on the other hand always flies in a straight shot from your character & it penetrates all enemies. Teeth's usefulness begins to fade away when you reach level 25 - 30 and start making your way into Act 4 and 5 at which point Bone Spear will be your primary ability.

This is how my talent trees looked when I was level 30.

Teeth wide spread. Cursor is close to character.

 

Teeth clustered spread. My cursor is further from my character.

 

Bone Spear penetrates through all enemies in a line.