First of all: although it's name is "iCloud", this is not a cloud storage. Apple's iCloud is used for backups. So if you delete something on your iPad, it will be gone in iCloud as well, and it doesn't really free storage space.
On an iPad, there's often the option to open a file somewhere else. It will look like this, when you tap it:
And then you get suggestions for apps that will open these files (mine was a video).
Tap the app you prefer. This will lead you to that app itself. Dropbox then will ask you if you want to save the file there.