If you don't claim the offer at the time of your first deposit, you can do so at any time within 30 days of registering your account. Simply log in to your account, go to the Account menu, choose My Offers then click Claim Now for the relevant offer.
Bonuses usually come with wagering requirements, which means that you have to bet a certain amount of money before you can withdraw any winnings that you make with the bonus money. Wagering requirements can vary widely from one casino to another, so it's always important to do some research.