When people get interested in mail, they generally want to make a byrnie first, which is like a mail Tshirt. What follows is a set of instructions and suggestions for making a byrnie. Once you have understood this, then you will be able to apply the same techniques to making other garments.
I have studied three patterns for a byrnie. The odd thing about these, is that they are all different, and yet they are all derived from the same period byrnie. Shirt O 1858 in the Wallace Collection, London, is a very good example of a mail shirt. An article I acquired some years ago ("Further research into the construction of mail garments" by E. Martin Burgess, in Antiquaries Journal) has photographs of it, and the photograph has the expansions and contractions marked on it. Another article on mail shirt patterns by Paul de Gorey gives us information on a pattern derived from shirt 920 of the Wallace Collection. I corresponded for some while with the arms and armour curator of the Wallace Collection, David Edge, and went in one day to look at shirt A2 of the collection. I handled the shirt in cottongloved hands, and made notes on the pattern.
It turns out that the shirt was called O 1858 when it was mistakenly catalogued with the oriental collection, but when it was proven to be of European origin (surviving European mail is very rare), it was given the number 920. When the Wallace Collection was renumbered, some years later, it was called A2. All three numbers, and all three patterns, therefore, are of the same shirt, which is German, made sometime around 1435 A.D. When I made my shirt, I was working from the Paul de Gorey pattern. I'll start with his pattern, and work from there.
Here we see the pattern I started with. The numbers are the number of contractions or expansions. You see that the shirt comes in at the waist and out at the hips. The groups of contractions, marked as triangles, involve one contraction in every fourth row. If you see a triangle with no number in it, that's because it is part of the same contraction the other side of the shirt. The sleeves narrow from the armpit with hole contractions.
Note also that whether something is a "contraction" or an "expansion" depends on your starting point. If you start from the lower edge, then you contract to come in to the waist, but working from the shoulders downwards you would call the same part of the pattern an expansion.
One important thing to notice is that the back of the shirt is eighteen columns wider than the front. Either side of the back are contractions of nine each. The main effect of this is to bring the armholes from the sides of the shirt, to the front. Human arms do not actually spring from the sides of the body, but they favour the front. If you think of your torso as rectangular in crosssection, then your arms grow from the front corners, not the middle of your sides. With an arm, you can reach across your front very easily, but you cannot reach across your back in the same way. Mail will expand freely until all the links are as far apart as they can go, at which point it stops stretching abruptly. If you put your arm holes on the sides of your shirt, as many people have learned the hard way, then when you bring your elbows together in front of your chest, the back of the shirt goes taut, halts your movement, and may even split.
A good way to start making a shirt is to make the contractions and expansions as separate pieces, then link them together, then fill in the gaps. You could, therefore, start with a rectangular patch of mail nine columns across, then contract this down to a point using the simple withthegrain contractions, ending in a single ring. If you put in one contraction every fourth row, the triangular piece would be 33 rows long. Here, I am using 'columns' to mean the lines with the grain that run up and down the torso, and 'rows' to mean the lines of rings that run around the body horizontally, against the grain.
I ask you to bear a few things in mind:
First, the number of contractions and expansions you will need to make will depend on the size of the links you are using. The smaller the links you use, the more contractions you will need. The Wallace Collection shirt has rings 0.405" in diameter, according to the catalogue (that's 1.03 of your ghastly centimetres, metric fans). I used rings with an internal diameter of 6mm, and so I increased the number of expansions and contractions as I saw fit. I'm afraid that I have no magic formula for working out by how much to alter the numbers, but common sense and judgement worked for me. My shirt weighs about 23 pounds (10.5 kilos).
Next, remember that mail, when made properly, with the grain running down the torso, will contract to hug the figure of the wearer. As is falls inwards to hug the figure, it lengthens. The fatter you are, the higher a given shirt will sit on you. This is unlike a cloth shirt. I gave a man the same height as me my shirt to wear, and whereas it comes down to my crotch, it came down to between his hips and the top edge of his pelvis. He was a fair bit stouter than I. The Wallace Collection catalogue says that shirt A2 is 28" long. I measured it as 30.5". Perhaps this difference is due to my having stretched the mail out, whereas it might have been more scrunched up when the catalogue author measured it.
Also, bear in mind that the shirt is not symmetrical. I thought myself clever when I made my triangular bits of mail as mirror images of each other (in terms of the direction of slope (the "lie") of the rings, as well as the number of rings), thinking that one would be for the right side, and the other for the left. In fact, of course, I had it wrong in my head. The pattern of the mail is continuous across the shirt, and so the pieces of mail I made should have been identical, not mirror images. I solved this problem simply by making one side of my shirt one column wider than the other, and I defy anyone to tell me, without many minutes spent counting links, which side is the wider. I generally had even numbers of rows between my contractions and expansions. This meant that my triangular patches were symmetrical, apart from the lie of the rings. Shirt A2 has contractions every fourth row, which means three (an odd number) ordinary rows between each row with a contraction in it (i.e. rows with "idle" rings  those that link to fewer than four other rings). This means that there is no centre link to the patch, and so the contraction has to be offset slightly to one side or the other (to the right, on A2, as one looks at the front of the shirt, so to the wearer's left).
Time for another picture, now, after all that text.

Here we see a moderately closeup shot of my shirt. One of the contractions shows up nicely. It is the front part of one of the long contractions that comes over the shoulder from the back. I've marked it on the right with a pink line. Note also the "latten" rings, which are the copperalloy rings which I have used to make the edges of the sleeves and neck hole look nicer. 

Well, this page is getting long, now, and I've a fair bit more to say, so I've decided to divide up the rest of the information on shirt patterns as follows: