It is important to make sure that the chainmail tapers correctly such that the outer edges just meet along the entire length of the vambrace. In the illustration above, I have shown a vambrace that is tapered to fit my arm in particular. Most people will find that a more even tapering will fit better, I just happen to have thin wrists, but YMMV. Measurement A should be the circumference of the lowest part of the vambrace, while B is the highest. C is simply the straight line distance from A to B along the top of the arm. I have shown in red, extra rings which should either be doubled up, or welded shut. It is through these rings that the lacing of the vambrace shall go. A slightly more advanced design would involve the addition of a leather lining either worn separately underneath the vambrace or sewn into it. In any case, a certain amount of experimentation will be required to get the dimensions just right.
In lacing the vambrace to your arm, I would recommend soft leather laces for the most comfort, but there are many options you can explore.
I have been asked on a number of occasions which direction the maille should sit on the arm. In truth, it doesn't really matter that much and is a matter of personal preference. I like mine to lay such that the mail pulls itself closed and tight when it is stretched along the length of my arm. If the mail is woven in the other direction, then the mail will have to be pulled to its most open position in order to achieve a tight fit when lacing.