I have an Orange Crush 15R with a headphone jack. I've heard that amps can be connected to computers/interfaces; can I do that with this amp? Could I just use a regular guitar cable and plug one end into the phones jack and the other into my interface? Or do I need another type of cable or adapter?
You can run the headphone out with a standard guitar cable, it will work. It won't sound too great, but it will work.
I think it would need a balanced 1/4" (aka TRS) cable. It'll work with interfaces, and not be too bad (though miking obviously would be the best solution).
Seeing as the amp is mono and just sends the same sound to both the tip and the ring connection, it works just fine with a 1/4" TS cable for connecting to interfaces etc.
True. As long as the cable's not too long.
So a normal cable into a DI box then into the pc would work?
Well, you'd get a clean guitar sound. That is good if you want to save your performance, and play it back later to your amp with a reamping device, or if you plan on using software amps.