Apple added Facebook integration to iOS with the latest iOS 6 update. Along with this, Apple made it very easy to post to Facebook and "tweet" to Twitter from the Notification Center with the addition of a Share Widget. Here is how you can share very easy from the Notification Center.
First head up to the Settings on your iPhone or iPad and look up for Twitter and Facebook. Tap each of these and make sure you have log in with your credentials.
Then head up to the Notifications area on Settings and tap on "Share Widget" and switch to "On"; this will make sure that iOS adds the Sharing Widget to the Notification Center. After this you are all set up.
When you are going to share to Facebook simply tap the "Tap to Post" area on the Notification Center. If you are going to share to Twitter, simply touch "Tap to Tweet".
If you want to share a photo to any of these social networks, go to the Photos app, select the image you want to share and click the share button; then select Facebook or Twitter. If you want to share a website link, tap the sharing icon on the bottom on Safari and select Facebook or Twitter.