This kind of t-tunic is simple, and period starting BC. Any stick jock can make one. All the seams are straight (except for the neckline, you're on your own), and the construction is straightforward. And just like in anything, measure twice, cut once. It's easier to make it too big and cut it down than make it too small and try to fix it bigger.
First, acquire or borrow a flexible (cloth, plastic, not metal) measuring tape. Then find a pencil and paper (graph paper is nice to draft your pattern on) and a friend to measure you. Your measurements will not be accurate if you measure yourself!
Measure from your shoulder to however long you want your tunic to be (to the floor is a period dress, at minimum, cover your crotch). Add one inch for seam allowance. Write this down as "A."
Next measure from the point of your shoulder to your wrist. Add one inch for seam allowance. This is measure "B"
Measure "C" is around your bent elbow. Add two to three inches for seam and room for movement. (On me, anything more than two is rather baggy.)
Measure "D" is around your shoulders (or over your breasts if you're female and that's larger than your shoulder measure. This will not produce a supportive garment.). Add two to four inches, depending on how loose you want your tunic. (Two inches gives me a nice fit, with enough room to move.)
Measure "E" is from your shoulder to waist. This will allow you to make "gores" so that your legs have room to move. If you leave the gores out, you will have an old-lady hobble skirt with top, not a tunic you can walk in.
Now take graph paper or regular paper and lay out your pattern. The main body piece has to be twice as long as measure A and half as wide as measure D. So twice as long as you want the whole thing to be, because it's folded in half; and half as wide as the finished product will be.
The triangles at the bottom of the body are called "gores" and give you room to move your legs. Those are as long as your waist to the bottom of the tunic, and as wide as you can get them. 6" is a good starting spot for a short tunic, a foot or more for a dress. Cut these after you've cut the body and sleeves. Cut two rectangles, (A-E) long and however wide, and cut on the diagonal.
The sleeves are as long as your arm and as wide as around as your elbow. My sleeves are almost square, so remember which is along and which is around, or mark with chalk. You can taper them, but leave that until you've made one or two.
The last pieces to cut are the "armpit gussets." Cut two squares 4-6" long and cut in half on the diagonal.
fabric
Your fabric will need to be at least 2*A long. I can make a tunic out of 2 yards of 45" wide fabric. If you aren't rail thin, buy 60" wide fabric. If it is hot where you live, buy linen (best: cool and very tough, soft after a couple washings) or a cotton woven (doesn't stretch when you pull along the grain)(not period, but almost as comfortable as linen and easier to find). If you live somewhere cold, make one tunic out of a light colored linen or cotton, and another one out of wool. Wool is magical wonderful fabric that will keep you warm even when you're sopping wet. This is nice in the winter. With an undertunic, your wool should last a good long while. Wash your linen or cotton on hot, dry on high, before you sew. The pre-shrinks the fabric so your finished garment won't shrink.
Construction
First, cut out all the pieces.
If you're using a facing to finish the neckline, do that first. It's my preferred method, but I can't explain how to do it. Find a local seamstress and ask them for help.
Take each sleeve and sew two gores at the top. If you made squares, it doesn't matter which leg you sew. The sleeve now has an ungusseted skinny end and a fat end, with two triangles sticking out at the top (like in the pictures above). Make sure to get the seams on the correct side.
Now put the gores on the body. Take the fat end of the gore and start sewing it to the bottom edge of the body rectangle. Make sure you get the square side next to the body piece, not the diagonal cut side. One in each corner, all the seams on the same side. The body rectangle now has two fat ends and tapers in the middle.
Find the middle of the body and the middle of the sleeves. Pin them together. Sew the sleeves on (seams on the correct side!). Now you should have fat ends on the body, sleeves in the middle. Cut a head hole and see if it works. It should look like a sleeved tabard.
Now sew up the long seams. Start at the end of the sleeves and work your way in. Make sure all the other seams match up. The hem (bottom) is the easiest place to fix mess-ups. Don't sew the sleeves or the hem shut!
Turn the bottom edge over and sew it down (or if you have experienced help, try to make the hem even!). Then roll it and sew it again, now your seam won't undo. Do the same with the sleeves.
Necklines are more complicated. You can cover them with bias tape (found at your local fabric store) or find a local seamstress to help you. If you decide to face the neckline, do this as the first step.
Congratulations, you've made your very own tunic!
If you want a different explanation, as well as not having to do your own math, try the T tunic Generator.