To get the Xbox Live Arcade you have to have a
Gold Subscription ($50 a year for a service that craps all over PS3 and Wii). So Xbox Live is a definate neccessity for any 360 owner. Then go and buy some XBox Marketplace Points (either via Credit Card or in-store) --- Its $20 for 1600 points (damn you MS why cant you just make things easy for us!) --- Each of the 'better' Xbox Live Marketplace games go for 800 points, so its $10 a pop --- expensive yes, but there's the added online play and stuff. Theres a bunch of games on there, so have fun!
Oh, and BTW you need an internet connection :P