How good do you want it to look and what tools do you have? If you have a table saw, you can build some nice stuff. A chop/mitre saw would help too but you can cut angles on a table saw.
I would make the face frames with 3/4" or 5/8" (actual). You can make grooves in this thickness to hold/attach 1/8" plywood pieces. Or you can screw 1"x1" (3/4" actual) cleats into the rear of the face frames to which you can attach 1/8" panels. RV manufacturers typically have double-walled side/end and bottoms on cabinets and you can use good-one-side finish plywood. Using cleats, you can screw them to walls and ceilings for structural support and then install the finish 1/8" plywood to hide it.
Cabinet doors (and drawer fronts) can be made yourself with 3/4" material and then use a 1/8" inset panel by cutting a groove/dado (on table saw) and making the inset panel free-floating.
Joinery can be done using cleats, brads, dowels, pocket screws, "biscuits" and/or glue. Methods will depend on available tools and skill level. It's not easy to explain how to do it in a few words here. Note that miter corners may not be a good idea if there is a large seasonal humidity change. Hollow bottoms and end walls can be a good idea for running wiring, lights & switches. If you have a specialty plywood supplier nearby, you might get lucky and find some pre-finished plywood to match existing finishes. Or get some unfinished oak, maple or whatever and stain and use some varathane on it.
If you do some googling, there's tons of how-to info. on RV cabinetry.