Like they've said, you have to gain access to your phone's filesystem somehow. On the phone itself, iFile is your best (if not only) option. When connected to your computer via a USB cable, you've got a few options. I personally prefer iPhone Folders though I don't believe it's been updated to work with anything past iTunes 9, so the next most popular choice seems to be iDiskAid. It should let you navigate your filesystem and copy files to and from your device.
Wirelessly, you can use WinSCP as long as your computer and iPhone are connected to the same wireless network. If you do this (which requires you to have OpenSSH installed), the default password is "alpine" but you should change that immediately if at all possible. There are tutorials online to help you with that.
Official apps all have long complex folder names. If your program doesn't show you the icon for the app, then I would suggest using SBSettings. In its "More" menu, you can select an app and have it show you the exact folder name where it resides. You can use that with iDiskAid or WinSCP to find the folder for Atomic Web Browser which is where your downloaded file should be somewhere.