Move your data to the clouds.
You cannot upgrade the iPad for more storage capacity or more memory which would be RAM. You want more storage capacity on the iPad. What you bought is what you get - there is no upgrading.
You need to start dumping content off of the iPad. Transfer some of the content into iTunes and backup the iPad. Then you can safely delete it on the iPad. You can always sync the content back at a later time.
How to backup and restore from a backup
When you go into iTunes (with your device connected) there are many options to choose which stuff is synced, for example not syncing your whole 'my photos' folder off your computer instead syncing just a few. Or to choose which albums or videos to sync instead of the whole thing.
You just have to manage your space and choose what you really want/need on your device.
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.
You could upgrade your motherboard like I did with my iPhone, but it can be costly. I only upgraded mine because my iPhone was dropped in the sea while on vacation.
Clearly the warranty will be voided, but it's cheaper than getting a new iPad, though selling it and using the money to get another may wield better results.