What you will need:
- Apogee Jam or iRig guitar interface adapter for iPad , iPhone, iPod touch, Android and Mac 
- Garageband (or other app for effects and amp like Amplitube) 
- iReal Pro

Steps:

- Launch GarageBand and create a new song (or similar app as above)
- Choose “Guitar Amp” and turn on the monitor
- Adjust gain

After that open iReal Pro and play along or tap on Share on the top right and select Record.

If you record with GarageBand or similar apps, export your iReal Pro backing tracks in WAV format which is now a very fast process.
Then select 'Copy' (or Audio copy in older iOS versions) from the share sheet options and paste it into GarageBand.

There are 2 solutions:

1. Open GarageBand, add a new track and select an Inter-App Audio app. Open the Instrument browser and tap select iReal Pro. Record the song from iReal Pro and a new track to record your playing.    

More info here: https://support.apple.com/en-us/HT202870

2. You can listen to/record any track directly from iReal Pro into GarageBand with Audiobus and use effects. 

You find a tutorial here how to record the sound directly into Garageband.

http://www.lynda.com/GarageBand-tutorials/Importing-audio-Audiobus/109363/144096-4.html 
In iReal Pro, go to More/Background Audio and make sure that it's set to ON.
For an audio app to run background audio, it would have a setting for background audio OFF/ON. To run another audio app in the foreground at the same time, this app must allow the background audio through (many apps do not do this so you have to check.)