It will really depend on which wallet you choose to use.  Each wallet has it's own method of generating and diplaying bitcoin addresses for you.  Please be aware, bitcoin addresses are not "account numbers".  It isn't like a bank account where you only have one (or a few) "accounts".

Many people choose to use a new bitcoin address EVERY time they receive bitcoins.  Most wallets make this fast and easy.  You just click the "New Address" button, create a label for the address, and just like that you have an address you can give someone to send bitcoins to you.  One of the many great things about this method is that you now know exactly who sent you how much bitcoin and when, since you only gave the address to one person and the transaction to that address is permanently viewable in the blockchain.