for common terms like daw and tracker, google is your friend
as for "how to make chiptune", there are many many many ways, all of them with specific advantages and disadvantages depending on what exactly you want to do. with most of these options there are pretty steep learning curves attached, and hardware investments to be made, so do some research, listen to artists associated with the different systems/methods, and play with a bunch of techniques before you go all band style
as for anamanaguchi, the reason their music is awesome and notable isn't just that they "used chiptune sounds with a band", it's that they are EXPERT LEVEL tracker musicians... combined with an awesome band. It's something that takes a lot of time. their method, I believe, is that Peter (or occasionally someone else) writes a ballin ass track in famitracker (NES tracker software for PC) and then they load that track onto a powerpak NES cart (a special NES flash cartridge) for live performance. and they they play, as a band, along with the NES track, triggering different song changes and various things using the NES controller.
this works for them really well, because unlike using VSTs or just loading "chiptune-esque" samples into a keyboard, they get all of the sonic details that makes chiptune "chiptune": bends, slides, phasing, tons of channel changes, intricate noise channel effects, etc., rather than just "band playing with square wave keyboard sounds".
eh, food for thought
