When I started in this business it was as a scenic carpenter. I don't mean a carpenter that is good to look at (although I remember one nice young lady who interned at the Park...) "Scenic Carpenter" is the general hand of the set-building trade.
As a scenic carpenter you are expected to be familiar with not just wood and standard theatrical construction (the muslin flat, the platform, the basic staircase), but also a fair bit of both house and finish carpentry (hanging doors, building cabinets), but also non-wood materials. As a carp I was also a welder with stick and wire (and a very small amount of gas), sculptor in styrofoam, chicken wire and glue-muslin, a fairly amateur plumber and electrician (for what we call "practical" set furnishings from desk lamps that light to sinks with running water), and a smattering of other materials and skills including laying tile, pouring concrete, threading pipe, casting with resin, running an industrial sewing machine, and so forth.
(Plus there is rigging and the basics of stage machinery...but that's a whole other subject).
Out in a medium-sized shop -- like Boston's Huntington Stage -- the carps are doing the more basic work as well as lifting and carrying, one or two are better welders than the rest and do the brunt of the welding, and one or two will be split off for most of a week on any special projects the Master Carpenter/Shop Foreman doesn't take for her own. Often you'll have one or two people who are better with finish carpentry as well, a handful of interns who are best kept putting legs on platforms, and part of your crew will "float" from building to helping the scenic painter and her team.
The connected field is props building. Most of the work of the Props Mistress (or Props Master) is wrangling, renting, and scouting for the things. Few companies can afford the time to build every lampshade and pocket watch, and there is no sense in building a dozen parasols from scratch when someone in the area has something that will work for purchase or rental (or that can be suitably modified).
Sometimes, though, you have to build it (and far more often, you have to repair it!)
As a props builder in a theater most of your labor will be things like spray-painting washers gold (to make heaps of quick-and-dirty money for a period show). Only every now and then do you have an important, detailed, actor-carried practical prop like Oaklahoma's "The Little Wonder."
In re that specific prop: The description in dialog is that it is basically a simple prism viewer with a folding knife. The dialog says you wait until the victim is holding it at eye level, unfold the knife, then shove his hands down and into his gut. Forget that. I made mine more of a Speed Racer gag; the knife comes out the viewing lens.
Mine was constructed from several pieces of nested pipe, PVC and steel. A rubber dagger was pressed against a spring and held there by a cut-off bolt running through an L-shaped slot. Turn the front ring, the bolt slips out of the "L" and travels to the end of the slot with a satisfying "chunk" of steel against steel; popping the spring-loaded blade six inches out the business end.
Practical props (aka props that have moving parts or other functions) are the most fun and the most difficult and also the least frequent build you'll have. More typical of the things I built was a fake speaker, painted Navy gray and mounted on the set for Mister Roberts. As I recall, the round body was sonotube, the bracket was 3/4" plywood as was the front ring, and the grill was expanded steel over cloth. The decorative bolts were 3/4" nuts roughly filled with hot glue and painted gray like the rest of it.
My proudest "build" was actually a rescue; the "Man of the Year" award broke on stage on Saturday night and I found the original mold in the props shop and pulled an all-nighter casting and painting the replacement to have it on stage for the Sunday matinee.
Since moving over to the Electrics side of the house (which is generally divided into lights and sound, the former being tasked with any electrical stuff that isn't stage machinery like a motorized turn-table, and the latter dealing with only those things that are part of an audio or video chain), I've not been building many props. Among other things, I don't have a scene shop handy anymore.
I have built a couple little things on my own, however. Last year I went on a small but personally expensive spree and bought more power tools than really should be installed in a small studio apartment. I'm still barely on the edge of what I could whip up with a good basic shop. It is amazing how fast you can work when you can shift from bandsaw, chopsaw, bench sander, drill press, etc., as you refine a shape.
I have hopes of doing some more personal props during the year. My last one was a monster; a thirty-pound full-scale replica firearm with moving parts. Talk about prop buildings involving lots of different materials and techniques; it included welding, brazing, hot-bending, plastrut, sculpting, detail painting, metal fabrication, and 3D printing.
But that's the direction I'm going now. I don't have connections to a theater right now that would want me to build big, complicated things for them. Unless they have moving parts or electronics...then it is possible it might happen. So instead I'm doing stuff for fun, for friends, and the sort of stuff used by the cosplay crowd.
Which was part of why I was learning to program the AVR; I wanted to have (and now basically do have) a tiny computer I could stick inside a hand prop that would sequence lights and sounds and motors in any way desired.
My desired project at the moment is some kind of fancy-looking science fiction gun. Not something from any existing movie or TV show, and not of the more common big and heavily weathered look; something that is more small and elegant and highly detailed like a 1930's cigarette lighter or a well-built machine tool.
The most likely next project is going to be making some M18 smoke grenade mock-ups. I'm just waiting on some empty smoke-in-a-can to come my way so I can cut off the lids, replace them with a resin cast lid/fuse adapter, and screw my eBay-purchased fuses into them.