There are several ways to make frameless plywood cabinets. The simplest is a butt joint, then a mortise and half lap joint and the latest is butt joint using pocket screws fasteners. A good quality glue is used at all the joints. A face frame is usually added onto which the doors are hung. These are usually biscuit jointed, but again lately, the pocket screw fasteners are more often being employed.

Raised panel doors are available in several species on Ebay. They are relatively inexpensive, save a great deal of work, and eliminate the need of purchasing expensive tools that require some knowledge and skills to master.

Plywood is a little more expensive than MDF, but it is easier to work with, takes standard screws for fastening, and it is stronger and a lighter material. There are grades now that are available in several species of wood and are prefinished from the factory. This greatly reduces your construction and finishing times.

There are many books and web sites that illustrate the construction of cabinets. Most big box stores have an assortment. A large selection of power tools is not a prerequisite, but a table saw greatly simplifies the construction.

Gard

Gard did a good job answering the question.

When I need to make some inexpensive cabinets ( ie. storage in the garage ) I usually buy some Baltic plywood in 5/8" or 3/4", it usually has thinner layers and has more layers, (i.e. 9 layers vs 7 layers which hold the screws/staples better ).  I build the box by Butt joining the edges with glue and a staple gun shooting inch and a quarter staples.  Before fitting together I rip a groove with the table saw that I slip the back panel into.  Usually 3/16" masonite. The groove is on all 4 pieces, ( 2 sides, top and bottom) Fit the sides and bottom together and just before attaching the top, slip the masonite into the groove.

Build your face frame out of solid lumber or plywood you have ripped down to size.

For simple doors, cut MDF or plywood to size and run a router around the outside edge.  If you want a nicer real wood look. You will have to laminate up several widths of hardwood to get pieces large enough to make doors out of. You just don't buy 18" wide planks of Oak, Maple or Cherry now days. The hardwood will take more work to glue up and you will need a planner to insure uniform thickness. Like Gard said, Just buy the fronts after you build the boxes.

Paint or stain, add the hardware and you are done.

MDF  = Medium Density Fiberboard

They basically take sawdust and mix it with glue and make MDF.  It comes in planks or sheets of varying thickness.

Most lumber yards stock it in 4" 6" 8" 12" widths in 16 foot lengths and in 3/4"  1" and 1 1/4" thick 4x8 sheets.

We use it a lot in new home construction.  Baseboard, casing, stair riser, Stair skirt boards, Window sills are all common uses of this product.  It doesn't have the strength of regular wood. So we don't use it for anything requiring structural strength. But very smooth surface and paints up nice. So we use it a lot for paint grade interior trim work.  Since you can buy it in 4x8 sheets, it's easy to make paint grade cabinet doors out of it.

MDF is medium density fiberboard. It is graded sawdust that is mixed with glue and formed into sheets. It is heavy, has little resistance to bending, most are not waterproof or even water resistant, and will not hold a standard wood screw. It is a poor choice of material when strength and light weights are a concern.

There are laterally dozens of books and pamphlets available for cabinet construction. Goggle "cabinet construction", try your library, woodworking stores, Lowe's or Home Depot. 

Gard

I made the face frame of my cabinets with solid oak and the hidden parts of plain plywood.  The large exposed face's I used 3/4 inch oak faced plywood from Home Depot.  For doors I purchased from this site. http://stores.ebay.com/DOORSANDPULLS_W0QQssPageNameZl2QQtZkm

Attached is a picture of my base cabinet.  Email me if you would like additional pictures.

Good Luck

Turfa

Hubby's been working on my cabinets for a couple of weeks now.  His nickname is "overkill" so imagine a very intense, detailed construction.  He has built frames into the dressing room using tongue and groove pine planks and has built the cabinet doors by gluing the planks together and fitting them for size.  I chose pine over oak to save a few pounds.  He's putting so much varnish on these cabinets, that I think it's a wash as far as the weight!  In HD or Lowes, you can buy pine (or other wood) boards that are already glued together and come in different widths and lengths.  They are sanded and basically ready to use, very pretty but they are pricey.  They would make nice doors.  I am using one for my counter top. 

Hubby would not use pre-fab ready made cabinets that are basically constructed of particle board.  He says the vibrations of the trailer in transit will loosen the joints and screws.  I'm collecting my pics of the LQ in progress and will post when complete.

Can't say there is an average or standard height for electrical outlets and switches.  It probably depends on your individual trailer layout.

Make sure hubby varnishes both sides of the pine planks and the joints. Otherwise they will unevenly absorb moisture and can warp across their width.  If you find a board with some pitch, such as near a knot, shake or heartwood, it can be removed with acetone before varnishing. Otherwise some of the urethanes will not cure properly.

Pine is a beautiful wood and will naturally darken with age. I'm sure your DR will be most attractive.

Gard

Gard... in this case, wifey is applying most of the varnish!... got to help out where I can, and yes it is going on both sides all the edges, corners, digs, dents, etc.  Did I mention we call him "overkill"???

Overhead cabinet and doors are now installed and everything is finish sanded and waiting for the last coat of varnish.  Last night I tooled a leather piece to glue onto an outlet cover.  I have Texas Star concho's for the cabinet door pulls.  It's really starting to come together.