If your amp has DIRECT or LINE LEVEL out, you can go from either of them to the DP- that is actually the best way to go.
You can run an instrument from the effects loop PRE-AMP OUT to the DP-01. I did it with a little bass amp and bass, and can hardly tell the difference between that track, and the same thing recorded thru the speaker and a SM57. Yeah, I was suprised, I expected the mic'ed track to sound more "alive," but they are almost the same.
If you make a mistake and plug into the POWER AMP IN, you won't damage anything, but no sound will result.
You could go from a headphone out to the DP, but phone signals are hotter than what the DP likes to see, so you will need to turn the DP's gain down- small chance it will still sound like crap, though.
But do NOT go from the speaker out to the DP-01. You will burn out circuitry on the DP-01, and it is probably not worth getting repaired.