Install Xcode 7 from the Mac App Store.
Download the source code for the app you want to sideload. Typically you will be able to download the entire Xcode project. For example, you might want to try an emulator like GBA4iOS or app that can change your screen gamma. There are many others. Check out this list.
Most applications can be downloaded as a zip containing the .xcodeproj. More complex apps may have dependencies that need to be installed such as Cocoapods. Read the instructions on GitHub or Bitbucket for assistance. Also, make sure to only download apps from trusted developers.
Double click the .xcodeproj file to open it in Xcode.
Select Preferences from the Xcode menu.
Click the + button under the Accounts tab then select Add Apple ID....
Enter your Apple ID and password the click Add.
Select the app project from the side bar on the left if it isn't already selected then change the bundle identifier to something unique. Typically you would use a bundle identifier that looked like 'com.yourname.appname'. For example, com.johnsmith.gammathingy.
Connect your iPhone to the computer via USB. If this is the first time you are using the device with Xcode, it may take 5-10 minutes for Xcode to setup the iPhone for use.
Choose Product from the menu bar then select Destination from the Product menu.
Select your device from the list.
Press the Run (Play) button to compile and run the application.
You will get a 'Failed to code sign' error. Press the Fix Issue button.
Select your account from the list of Apple ID accounts and press Choose.
The app will now install on your device.
If you get an error that reads "process launch failed: Security", tap the new app icon on your device.
You should get an error that reads "Untrusted Developer".
Tap Cancel then tap Settings, go to General, then go to Profile.
Select your Apple ID from the list then tap to trust your Apple ID. Press the Trust to confirm your selection.
You can now go back to the SpringBoard and launch the app.