You can't increase it. You can use any number of different methods to reduce your loading, moving some of your content off to either storage you control locally or to cloud storage remote from you. Basic web searches will let you locate and examine most of those options; many offer limited amounts, in the range of a few GB's, of free storage, but from the sound of things you will need something more than that.
You can increase the "free space" on your iPad in iTunes.
1. Go to iTunes and select your iPad from the selections on the left side of the screen.
2. At the top of iTunes, you'll see a number of tabs (Summary, info, apps, etc)
3. Select the "Apps" tab and click "Sync Apps" and unclick any app that you do not use frequently
4. Select the "Music" tab and click "Sync Music" and click on the playlists you really need on your iPad
5. Select the "Photos" tab and click "Sync Photos" and "Selected Folders" and click on only the photos you really need on your iPad.
6. Sync your iPad by clicking "Sync" or "Apply" at the bottom right of iTunes
7. By performing the steps above, you'll have more free space to download a movie
You can do this with the other tabs as well. All of these selections can be changed later.
Movies take about 1 to 4 GB, so you need to free up a lit of space. You needed to have bought a 32GB or 64GB iPad.
How much space is your Other using? You may be able to reduce.
How Do I Get Rid Of The “Other” Data Stored On My iPad Or iPhone?
With an iOS device, the “Other” space in iTunes is used to store things like documents, settings, caches, and a few other important items. If you sync lots of documents to apps like GoodReader, DropCopy, or anything else that reads external files, your storage use can skyrocket. With iOS 5, you can see exactly which applications are taking up the most space. Just head to Settings > General > Usage, and tap the button labeled Show All Apps. The storage section will show you the app and how much storage space it is taking up. Tap on the app name to get a description of the additional storage space being used by the app’s documents and data. You can remove the storage-hogging application and all of its data directly from this screen, or manually remove the data by opening the app. Some applications, especially those designed by Apple, will allow you to remove stored data by swiping from left to right on the item to reveal a Delete button.