Instructions
Use the "System Update" feature on your console. This may be required after the PlayStation Network has gone down for any type of official maintenance period. For example, after the PlayStation Network went down in April and May of 2011 (during which all users worldwide received a 80710092 error), the only way you could log back into the PlayStation Network was to download the official firmware update for the console via the "System Update" feature.
Check the official PlayStation Blog to make sure that the PlayStation Network isn't down for any type of routine maintenance period. The error message can be received if the problem is with something you're doing but also if the problem comes from the fact that the network was intentionally brought offline by Sony. If the PlayStation Network is undergoing a routine maintenance period, the official PlayStation Blog will have details of how long that period is expected to last. After the period is over, the error message will disappear and you can get back online.
Make sure you are signed into the PlayStation Network. Go to the "PlayStation Network" option on the console's main menu and look at the top menu listing. If it says "Sign In," you have been automatically signed out of the network. Select "Sign In" and type your email address and password to sign back in. If you played a Blu-ray disc or a DVD on your console since the last time you used the network you will have been automatically signed out which can result in the 80710092 error message when attempting to play a game online.