At what point can I start playing against the bosses in Naxxramas successfully?

I recently started playing Hearthstone.

Today I tried the first Boss in Naxxramas and got really smashed.

What do I need before even trying to beat the bosses?

Solution 1:

Once you have unlocked and leveled up all the heroes to 10, you will have all the basic cards at that point.

Its possible to beat all the bosses (non heroic though) using only basic cards and some luck with the draw.

Solution 2:

I used this deck to defeat the first 6 normal mode bosses. This deck won against each boss on the first or second attempt (many times in close contests).

Mage

Arcane Missiles
Ice Lance x2
Elven Archer x2
Mana Wyrm
Frostbolt x2
Amani Berserker
Kolbold Geomancer x2
Millhouse Manastorm  (Legendary)
Arcane Intellect x2
Frost Nova x2
Mirror Entity
Cone of Cold x2
Polymorph
Water Elemental x2
Azure Drake x2  (rare)
Stampeding Kodo  (rare)
Archmage
Frost Elemental x2
Reckless Rocketeer
Ravenholdt Assassin  (rare)

There are four rares and one legendary. Millhouse is just for fun and a Raptor will do in his place. The Ravenholdt could be an ogre or golem. Replacement for the Kodo is unclear, but you're looking for a nice two for one card. Replacement for Azure Drake could be Gnomish Explorer.

To answer your question: if you've opened enough packs to have a few rare cards, I'd say you are well prepared for Naxx normal mode.

Update: I've gotten through Patchwerk with this deck so far. Some fights are very difficult with it and a matter of playing until the right cards come up.