The Combined Field System is pretty much the equivalent of the Star Trek
Warp Coil (not to be confused with 'Warp Core'. The CFS isn't about power generation; it's about creating a subspace bubble that distorts the space-time continuum of the ship, allowing it to propel it at velocities beyond the speed of light).
Historically in the SARP, it seems the CFS is really a big gyroscope-like structure encased with a spherical cover. How it actually functions is beyond me. But the effects it produced are explained in the CFS descriptions, so that's pretty straightforward.
What technicians can do about it - that's what you really want to know, right? The Miharu's CFS units haven't actually sustained damage, so, most of the mechanical work isn't really needed. You don't need to disassemble the unit and replace something. The problem likely lie more within the adjustments of the way the fields are made (just like the way warp field geometry works in Star Trek).
The Miharu's four CFS units already work below specs at the ~190 000c speed, but the shock they sustained from the Mishhu anti-FTL field and the hot-restart decalibrated them. The MEGAMI re-tuned them as much as she could while remaining within safety parameters. Chigusa's and Leutre's job is more or less to work at the unit's console and try to tweak it to get performance up by making adjustments here and there - mostly software... but there should be some hardware work too (scan specific power relays for faults, adjust consequently to compensate/juryrig, swear to fix them properly in space dock, etc etc...)
However, the units must remain running, making the work on them even more painstaking because if they suddenly fail, it'll possibly hinder the Miharu while the ship is already outnumbered and outgunned.
You can dig around the stuff and terms behind Star Trek warp cores and use them - I don't think they'd be too far off (since apparently CFS technology is derived from what the SARP got from the 'Python Sector' roleplaying universe... which was Star Trek-based). If Wes wants to establish something more solid, we'll follow that... but Star Trek should really be your best reference for technical terms with anything regarding the CFS units.
Just remember power generation is obtained through a zero-point energy generator, not dillithium cristals
Hyperspace Fold is something entirely different.