How websites like silkroad and pandora process transactions? I've been reading about Bitcoin on the news and I decided to learn how it works. I'm sorry if I'm posting dumb questions.

How these websites process transactions? How can they monitor one or more receiving addresses per registered users? Do they use custom software that interacts directly with the blockchain?
The underlying mechanism is to generate an address specifically for one payment. The address space for Bitcoin is mind-boggingly large (almost any 256 bits number is an address) so that's not an issue. That address is monitored for a payment and once the payment is received, automatically transferred to the merchant's final address (or payment).

As to software, it's a bit all over the map. You can either use something that will make the whole process transparent (like BitPay or Coinbase) or use lower-level APIs interacting with the BlockChain like BlockCypher.