I'll try to explain how I did my cabinets.

I didn't use a base on the cabinet, space is at a premium in a teardrop and the base isn't needed.
I decided on how I wanted my cabinet doors and drawer positioned then made a face frame. The face frame is what your cabinet doors are attached to, typically made of 1 1/2" wide x 3/4" thick wood, joined together in a kind of "grid" with openings for your doors and drawers. The vertical piece on a face frame is called a "stile" and the horizontal piece is called a "rail".
Because not much is "standard" on a custom teardrop, you make everything fit with as much usable space as possible. The outer stiles on the face frame in my galley are 3 1/2" wide instead of 1 1/2" so the cabinet doors can swing open fully 90 degrees without hitting anything. The main thing when building your cabinets is take your time and be sure your cuts are square and if you have two pieces that need to be the same dimension lengthwise, make sure they are. Little errors add up to be big errors.
I used a Kreg jig for making pocket holes to join the face frame pieces together. It's a quick and strong way to build. I also used the pocket holes to attach the face frame to the teardrop sides and floor. If you notice in the photo, I screwed a scrap piece of material from the ledge at the rear to the face frame to support edge of the countertop. I just used 1/4" luan plywood to make dividers between the door openings on the face frame. Try to keep things as light as possible, but still strong.
Overlay doors are simple to construct and they are made a little larger than the door opening on the face frame and are very forgiving. You don't have to try to fit the door to the opening like on a flush mounted door. I used simple wooden turnbuckles I made to hold the drawer and doors shut while traveling. There are many ways to do this, but my galley has a rustic look to it. I found suitable hickory sprouts that would work for my pulls on my cabinets and used those in place of store bought pulls.
You can probably find some good books on cabinetmaking at your library. Most will be a lot more information than you need for a set of teardrop cabinets. Again take your time and plan out what you want in your cabinets before you start cutting.
As far as tools go, for a basic set of cabinets you could do everything with probably no more than a drill, tablesaw, tape measure or folding rule, screwdrivers and some clamps. A router would let you make some nice edges on your cabinet or you can get a stile and rail bit set and make cabinet doors similar to what the cabinet shops produce. I really would consider the Kreg jig too. That is one purchase I made that I don't regret. I use it a lot, but I'm always building something. You always have the option to buy your cabinet doors instead of making them too. There's nothing wrong with that if you don't want to spend the time or money to make your own. The face frame and cabinet and drawer boxes are easily made.

I hope this helps you somewhat. Just break it down into small projects. Draw up your plan. Build your face frame. Build a drawer box., etc. and pretty soon you will be camping in style!
Lynn