This wonderful device plugs into to the 30 pin dock connector. Infinitely superior to the plug into the headphone jack crap devices. It allows one to connect a guitar, stereo input, microphone headphone/stereo out. Sturdy, marvelous, diligent googling will find it for about $100. Download the free GuitarTone app to control the GuitarJack and get a tuner and several amp and effect simulators thrown in that are available free when the app detects that a GuitarJack is connected.
Garage Band cheap, can't imagine an iPad musician that doesn't already have it. The guitar jack works perfectly with GarageBand. The guitar amps and effects built in aren't bad.http://agilepartners.com/
I have two apps from this company: Ampkit and TabToolKit.
Ampkit provides some very good amp and effect simulators. Free to start but in app purchases could add up. I'm waiting for Black Friday/Cyber Monday sales to load up. Has recording built in. Allows playback of music while you play along. Speaking of which http://www.guitarbackingtrack.com/
Karaoke for guitar! 100s 1000s? Of songs with the guitar parts removed. Free! Loads into Ampkit. I use an app called GoodReader to download music, video, PDFs, zip and almost everything else Apple tries to force me to buy from iTunes. Extremely useful for every iPad user.
Also from the makers of Ampkit is TabToolKit to learn the song before you try to play along. Loads guitar tablature in many different formats. If the Guitar Pro or Tab Pro formats are used it will play back the song as it displays the music notation, the tab, the guitar neck, and even displays drum, bass and keyboards. Dial in the sound in Ampkit and learn the tune in TabToolKit.
Rock out with the headphones and not bother Wendy or the dogs or the neighbors. Even use the iPad as an effects box when I go over to a buddies studio. Plug into the mixing board or an amp.