You can buy cards at stores worth Microsoft Points. Usually you'll find 1600 points for $20, very few places sell just 800 point cards.
You would redeem a code on the point card to get the points on xbox live and then go onto the marketplace and buy the DLC with the points.
Not sure what you mean exactly with question number two so I will answer it best I can.
You can use an ethernet cable($20 or less) and connect to the internet and xbox has a silver account and a gold account. Gold is only for playing Multiplayer games and some stuff is only available if you have a gold account such as Netflix and some special sales on games and dlcs.
Silver is free. Somewhat limited, but thats all you would need. You cant party chat, but you can private chat. You can still have friends and download dlc and demos and games with silver.
Playing:Far Cry 3,Final Fantasy XIII-2. Mass Effect 2 and 3. GT: Rainingoblivion
Sweet, so what you're saying is that I can just disconnect my computer from the internet and use its cable on the 360 and I can use Silver and Microsoft point cards to download the extra content. Thanks for the help.
Go ahead, believe everything the media tells you, they would never lie to you, right?