OK so it is a bit hard for me to use a device without apps. I looked around and experimented with several things, and finally found how to install apps from an APK file. I will split it into two tutorials. The first one being for iOS, the second one for iDroid. Note: There are two types of APK files. The first one is an installable, pre-packaged file. The second one is an already extracted file, which cannot be used with this method.
How-To for iOS:
-Boot into iOS
-If you haven't already, launch Cydia and install OpenSSH.
-Install and open WinSCP on your computer.
-SSH into your iDevice by following the steps below:
--Log in using your phone's IP address (192.168.x.x, which can be found by connecting to your WiFi network and going to Settings->Wireless->Tap the blue arrow next to the network you are connected to->Look next to IPv4. Copy this down or remember it in your head.
--Enter your phone's IP address into the Host: box, and for username put "root", and password put "alpine". (you should change the password later. I won't include this.
Visit this link to find out how to change it.--Click connect. If a box comes up with a lot of text, click Yes.
-In the first pane, navigate to the directory you downloaded the APK to.
-In the second pane, go to /private/var/sdcard/download. (correct me if I am wrong on the /private/var part)
-Drag and drop the APK.
-Right click on the APK, click properties, and change the permissions to 777. Repeat with the download folder, and sdcard folder.
(Note: you only need to change the permissions of the folder one time. You must change the permissions of each APK, however.
-Close the connection by exiting WinSCP.
-Boot into iDroid, open the file manager, navigate to the download folder, tap the APK, confirm, and it should install.
How-To for iDroid:
Instructions coming soon.