In order to win, all you need to do is take part in that weekend's event competition. Each time you complete the objective, you'll earn a ticket that will enter you in the prize drawings up to a maximum of 10. You can take part in each competition every weekend from now through August for a number of different prizes and the grand prize drawing after the final weekend of events has concluded.
This weekend's event is victory at Black Garden, so head over to the Alienware Arena website to sign up and find out what else you can win by competing in this summer's events.
Source: Alienware Arena Competition Page