Make sure the battery is fully charged
Use the 10W USB power adapter that came with the iPad and charge it for at least 20 minutes.
Check your hands
Don't wear gloves, use wet hands or use it immediately after putting on lotion.
Remove the protective sheet
If you have a protective sheet on the screen, try removing it to see if it responds better.
Try a power cycle (turn it off and back on)
Hold down the Sleep/Wake button on the top until you see the red arrow with the "slide to power off" prompt. Slide that arrow to turn off the ipad. Then turn it back on by holding down the Sleep/Wake button again.
Try a hard reset
Press and hold the Sleep/Wake button and the Home button at the same time for at least ten seconds, until the Apple logo appears.
A single application freezes when opened or is frozen now:
Press and hold the Sleep/Wake button until the red slider appears. When the red slider appears, release the Sleep/Wake button. Instead of dragging the red slider, press and hold the Home button for six seconds.
Delete the app and reinstall it from a Mac
Tap and hold the app's icon until it gets wobbly. Click on the x to delete it. Now tap the Home button to stop the wobbling. Plug the ipad into Mac with the USB cable and fire up iTunes. Select the iPad in the source column on the left and click the Apps tab in the iTunes window on the right. Find the app you deleted and make sure its checked. Click the sync button at the bottom.
Install the app directly from the iPad
Delete the app like above. Launch the app store from the iPad, find the app in the store and redownload it. iTunes should not charge again if there you've already purchased it.
Try opening the Settings app, then tap General, tap Reset, and tap “Reset Network Settings”--this will reset all your network settings to the factory defaults. Please note that when you perform this reset, you will lose your saved Wi-Fi secure network passwords. You can re-enter them later when connecting to that network again.
Do a Full Restore (last option)
This removes all apps AND settings. Plug the iPad into iTunes. Control-click on the iPad in the source list and choose Backup. Wait until its done. Then, control-click again on the iPad and select Restore from Backup and choose latest backup. This procedure may take more than a few minutes.