Start by getting the Lightning to USB Camera Adapter. (For older iPads, the 30-pin to USB Camera Kit also works.)
Get a SMALL USB-based MIDI controller, e.g. 25-key. Some MIDI controllers have batteries to power them, or larger professional keyboard controllers/synthesizers/pianos have their own AC power supply.
Get a CoreMIDI-compatible app, e.g. Garage Band, Tabletop, NanoStudio, MusicStudio, Thumbjam, etc. IMPORTANT: Launch the app.
Connect you USB cable to the keyboard and the Lightning adapter.
Plug the Lightning adapter into the iPad. IMPORTANT: Always launch the app first before connecting the Lightning adapter! If the keyboard isn't working, unplug and re-plug.
Tap some keys on the keyboard or the control buttons to make sure power is getting to the device.
Troubleshooting: some apps require you to tell them your keyboard is used for input.
Troubleshooting: some apps have "Learn Mode". Enter Learn Mode, tap on the part of the screen to "learn", then press your keyboard or twist a knob to assign it. Exit Learn Mode and play around!