As I said in the post where I talked about all the classes the Assassin Class is exactly what you expect of it. Assassins focus on single target elimination using sniper rifles or melee weapons. The assassin is also proficient at using other weapons, but has specific upgrades for melee and snipers.
Zero is the generic Assassin Class name in Borderlands 2, but you can customize the name and some aspects of the appearance of your character. You have to do that before you start the game and I think your choices are permanent.
If you prefer to listen to this post check the video at the end of this post.
Sniping (Accuracy and Critical Hit)
A lot of the upgrades from the Sniping skill tree aren’t specific to certain weapons. The later buffs are, but the first ones are to do with critical hit, damage and accuracy bonuses. This means that in the early game you can use a weapon of any type, but later you should start to focus on Sniper rifles should you wish to go down the sniping skill tree.
Cunning (Mostly Melee and Sniper)
This skill is mostly focused on buffing your melee damage. It also gives some buffs to guns, but most of them are especially useful for sniper rifles.
Bloodshed (Melee and Continued Damage)
Bloodshed focuses on either melee damage or different buffs to guns. It focuses on keeping you going, giving you damage buffs after a kill. Bloodshed also offers some health upgrades which are good to increase your survivability. Probably unnecessary if you play on the easier difficulties.