Run a Connection Test
If you suspect that Xbox Live is not working properly because of your Internet connection, run a connection test to see whether your signal, adapter, or network settings are malfunctioning. To get to this area, go to the System menu and then select "Test Xbox Live Connection" from the menu. Select this from the list, and the connection wizard will launch automatically. As the test progresses, you will see a "confirmed" status next to the settings that are working correctly, and a "failed" status next to those that are malfunctioning.
Check for Outages
As with any large online network, Xbox live does go down on occasion for routine maintenance. If you subscribe to the Xbox Live Newsletter, you should receive notification of this outage a few days prior. If you do not, check the official Xbox website (see Resources).
Renew Subscription
If it has been more than 12 months since you purchased an Xbox Live subscription, then you are probably being denied access to Xbox Live because your subscription has expired. To purchase a new subscription, open the player menu by pressing the Xbox button (in the center of the controller) and then selecting "upgrade to gold membership" from the menu. Then enter your credit card number, and you can purchase a 3-, 6-, or 12-month subscription to the Xbox Live service.