First you'll need a straight line from end to end along the barrel. The easiest way to do this is to lay the flute on a table up against the straight edge of something like a smooth board or maybe the binding of a book. Hold it still and you shouldn't have any trouble marking along the edge of the board. You may as well mark the whole length, since you'll probably want to line up the embouchure with the tone holes.
You can leave the flute blocked like that while you measure and mark the centers of the holes. It's usually best to make measurements from a mark on the line rather than from the end of the pipe, since the mark will have nearly the same parallax as any other point on the flute's surface. Check often to make sure your ruler is still in place with regard to the original mark, it's easy to slip when you're working with round stuff.
I marked what kind of pipe and what key the flute was to be in along with the measurement marks. Then I flipped the jig over and made marks there for a different flute. Each such simple jig is easily used for two (or maybe more if you mark in color) kinds of flutes. Of course, you won't want to make a jig until you've got your flute design pretty well settled.
If you're using the end-cap like Mark Shepard's Plumber's Pipe, you won't need to insert the end plug. Otherwise, make sure that the end you put in first will completely close the pipe. If it's a rubber stopper or a cork, just lightly set it in the end of the pipe and you'll know where you'll need to cut the small end off. The large end may be too large, if so cut some of that off too. Push the stopper or cork into the end of the flute up to somewhere within half an inch of the embouchure (mouth hole).
Bring the embouchure up to size and shape it into an oval or rectangle, whatever your preference. The walls of the embouchure should be parallel to each other, though you may wish to undercut the edge that you'll be blowing against. Not too much! Boehm only recommends seven degrees, and you can hardly get that right by eye. The top edges of the embouchure should not be beveled. Just take the burr off and leave it with a fairly crisp edge.
De-burr the tone holes somewhat, inside and out, just so you can close them with your fingers and so there isn't any stuff hanging inside the flute. Don't worry about smoothing them much, since you're going to be widening them anyway. Cover all tone holes and blow INTO the embouchure to clear all the junk out.
If you're using a stopper or cork re-adjust it so that its inner face is within a quarter inch of the closest edge of the embouchure. The placement of this stopper is what will determine whether your upper and lower registers are in tune with each other. (This is why I don't recommend the end-cap, it's not adjustable.)
Cover all tone holes and blow across the embouchure to produce the lowest tone. Tune that tone against whatever pitch standard you're using (a piano or electronic keyboard will often do nicely) by trimming the end of the flute away to raise the pitch. Then lift the finger closest to your mouth to get the note an octave higher. If the higher note isn't a perfect ocatave tune it by adjusting the stopper. Blow harder to get the second octave above your bottom note. That should really show whether you've got the stopper adjusted right.
Tune the tone holes from the lowest (farthest from the mouth) to the highest (closest to the mouth), one at a time. Check your tuning in the upper register as well. The pitch of each note should start out being a little flat. Raise the pitch of each note by widening the open hole just below the lowest one covered. So for the bottom note you tune by trimming the length of the flute. For the next note up you tune by widening the lowest hole. For the note above that you widen the next-lowest hole, etc. Play a little tune on the flute every once in a while and listen for notes that don't sound quite right.
All the while you'll need to make sure you don't have any big burrs hanging
inside or preventing your fingers from making a good seal when closing the
holes. When you've got the tuning where you like it you can spend more
time smoothing the holes with small files or sandpaper. Remember that it's
probably best to sand plastic underwater to keep that dust out of your
lungs.
I took a GIF of myself and converted it to black-and-white, printed it out on a laser printer, then transferred it to my flute. Remember, your image will be a "mirror" of whatever you print so you'll have to flip lettering before printing it out. Using a computer works so much nicer than trying to do all this with a copy machine, but you could get similar results with a copier using a transparency sheet to do the flip if necessary. The hardest part is getting a nice, clean image with good contrast. I've found that enlarging the image, cleaning the enlargement manually, then reducing it again gives good results on a computer.
Once you've got your image ready and printed out on paper, prepair the flute's surface by making sure it's smooth (I use 600 grit wet/dry paper). Then clean it and wipe it dry with a cloth. Wrap your paper image tightly against the barrel and get your fingers out of the way. With a candle flame, a lighter, or a heat gun try to heat the entire back of your image as evenly as you can for a short time.
Do not try to peel the paper away. Instead, immerse the flute in cool water and rub the back of the image gently. The paper will gradually disintigrate and as you keep rubbing you will eventually be left with nothing but the freshly decorated flute.
Trying to use this process on the end joints or other imperfectly cylindrical surfaces probably won't work well because the paper won't be able to lie perfectly flat against it over its entire surface. Using a hair dryer might work if it gets hot enough, boiling water could be used too if the image is well secured. Fine-grained or glossy paper may give better detail, but I haven't needed to try it.
Also, if you're willing to pay a little more your local copy shop may have a color copier (or better, a color laserjet printer) which allows you to make your transfers just as easily in full color! Note that color inkjets won't work because they don't use xerographic toner.
Be careful though, acetone will soak into the plastic and make it soft. This effect can be used to advantage if you want to make carving easier or even if you want to bend the tubing. I tried filling a pipe with acetone (stopping both ends with cork, not rubber) and found out the hard way that as the CPVC absorbs the acetone it expands. That caused internal pressure which eventually ruptured the pipe but left it with a beautiful, wood-like texture when it dried and the rupture closed up so well that I can't see it.
Softening CPVC enough to be bent may take as long as twenty-four hours. Drying out afterwards can take almost a week as it gradually regains its original hardness. I found that with the usual 1/2" CPVC pipe a turning radius of ten inches was a bit too tight (it wrinkled a little). Note as well that the pipe never did shrink all the way back to its original thickness though all of the acetone has evaporated.
Remember that you'll need the body to be longer left of the embouchure to leave room for the left half of the joint and for the stopper. The end joint should be placed so that the embouchure will be centered in it and the main body tube should protrude roughly half an inch out of the left side of the end joint, like so:
The stopper can be rubber or cork, whatever you prefer. Cut off the small end so that its smallest part only just fits into the tube, making sure that you have enough length left to keep it stable within the bore. You may need to cut, shave, or grind it down to a more cylindrical shape (rather than conical). Make sure that it fits snugly enough that normal cleaning won't dislodge it. The best way to position it is with a dowel just smaller than the bore and long enough to work the stopper even from the long end (for tuning or removal).
Begin with the normal flute design, adding length to the pipe beyond the head-end plug. Just above the plug, bore a small hole. Then file the side of the pipe flat between the hole and the embouchure. Don't file above the upper hole nor below the lower one. Undercut the lower hole slightly so that its outside edge is sharper. (I'll fix the diagram soon.) Push the end-plug in so it rests between the two holes. Using a reamed-out end joint (as was used for thickening a normal embouchure), slide it onto the pipe so it completely covers the top hole and rests just above the embouchure. See the following cross-section and top-view:
The player blows into the head end, like a whistle. The air can't pass the stopper, so it goes out through the top hole and passes across the filed-away space between the pipe and the end joint until it escapes, directed across the embouchure. Adjusting the end joint up or down may improve the performance of the fipple.
I've found that 1/2" grey PVC electrical conduit fits very snugly onto 1/2" CPVC water pipe, so I just use a short section of that instead of end joints. Just as with the fancy lip-plate, it's not necessary to completely surround the pipe. A quarter-round segment would probably be enough if it were secured with cordwork or straps. I wouldn't trust glue to hold anything less than half-round, and then only if the materials were the same.
You can also wrap sections of your flute with thread, string, yarn or whatever like traditional Japanese flutes are sometimes wrapped. I'd suggest using plastic model glue underneath to hold it in place. Apply the glue sparingly or the solvents it contains may "melt" the pipe.
Different surface textures can be gained with sandpapers of different grits, wire brushes, etc. If you make your flute out of metallic pipe you could chemically etch it but I don't know of a way to "etch" CPVC. The standard advice applies; work from your roughest tools (drills, knives) first down to your smoothest (files, sandpapers) last in gradual steps. For metals and plastics there are fine buffing compounds which will work a smoothly sanded surface to a glossy finish. Hardware stores sell those too.
There are polishes for metals, to help maintain the shine. For plastics you can use no-wax floor treatments. Some of them purposely leave a coating, others are meant more as cleaners... use whichever suits your purposes but be careful not to allow build-up inside the bore.