...which I understand to mean that they don't get class levels for the first two HD of their lives.
This is incorrect. What is means is that at level 1, when you have 1 class level, you add the +2 LA and so you are technically considered a level 3 character (ECL = Effective Character Level). And, according to the designers at WotC, you should only be adventuring with other level 3 characters, even though you only have 1 HD / class level.
You will figure skill points, saves, hit points, etc. exacly as normal for a level 1 character.
When the DM starts handing out XP, you do not need only 1,000 XP to go from level 1 to level 2. Sadly you need to amass the total amount of XP to hit ECL 4: 6,000.
Though, since you mentioned this is specifically a drow game, my hunch is that the DM will waive the +2 LA for everyone. Does not make much sense to use LA when everyone in the group is the same race / power level.