Free Up Space on Your iPad
There are many guides on the net that suggest removing photos, music and videos that you don't need, like its some kind of revelation. This guide credits you with some kind of intelligence and assumes you have already done this.


Apps
The first step is to check is what is using up all your storage. So open Settings and tap on 'General', then 'Usage':

SD

Some apps can take up a huge amount of storage. Some start small and increase over time. Delete the ones you aren't using and reinstall others. Reinstalling removes all the temporary data such as images and videos that are cached by many apps such as newspapers and twitter. Be careful with games as reinstalling will oviously remove cached scores and saved games.


Video
Video takes up by far the most space. One HD movie can take up 3GB of space. Consider using SD and lower resolutions.


Use the Cloud!
Web based storage can be used for music and photos that you don't need instant access to. I wouldn't recommend using it for video as only 2-5GB is free and downloading a movie can take ages.


SD Cards and Wireless Storage
You can now get 128GB SD cards (that's a lot of video storage) which can be connected to your iPad with a Camera Connection Kit. A more expensive option is a wireless storage device.


The dreaded 'Other' storage.
There has much discussion in the apple forums about 'Other' storage. Every video, picture or file sent in a message or received in a message will save in 'Other' even if the file is in your 'Photos' as well. Delete your music by going to Settings>General>Usage>Music (swipe left and select "delete"), then power off the iPhone and resync your music from iTunes. If your Other storage is still high then your only option is to backup and restore the iPad:


Backup and restore
If all else fails you can try backing up and restoring your device to clear out the 'junk'. iCloud and iTunes can back up most data on your iPhone, iPad, or iPod touch. Backed-up information includes iTunes purchases; photos and video in the Camera Roll; device settings (for example, Phone Favorites, Wallpaper, and Mail, Contacts, Calendar accounts); app data; Home screen and app organization; Messages (iMessage, SMS, and MMS), ringtones, and more. Media files synced from your computer aren't backed up, but can be restored by syncing with iTunes. Take a look at the official Apple Guide