Right now I have 0 credit since I've never had a credit card before, I recently applied for a credit card and got approved so I can start building my credit. I hear that 500-600 is considered very bad credit. Since right now I have a credit score of 0, does it slowly build up, does it go to 100 then 200 then 300, or does it jump to an average of around 600 then go from there?
The FICO score ranges from 300 to 850, and as a practical matter it's rare to be at the extreme low end of the range.
You may jump in with a decent credit score before long, as you accumulate a little credit. However, significant factors in credit scoring are the length, depth, and breadth of your credit history and recently opening credit accounts - so it takes time to build up a durable credit rating.
The credit score algorithms are proprietary, so no one can tell you for sure what your score will be. However, if you look at a distribution of credit score, the median score is roughly 710-730. You will likely be below this due to a short credit history etc., but are unlikely to be at the extreme low end as well as you don't have any "strikes" against you such as late payments etc.
Also, some utilities as well as student loan companies will report payment or non-payment of bills, so if you have any of these you may have a credit score even if you don't have a credit card.
As long as you pay on time and keep your level of installment debt low, you should be ok. See the following link for more information about how your FICO is calculated here.
Also, most lenders look at additional factors besides your credit score, so don't assume you can't get credit without a FICO score (or with lower than average credit) if you work with someone who will manually underwrite you for a loan.