If adding chainmail over clothing, simply stick and flatten a piece of putty where you want the armour to be; if replacing other armour, be sure to scrape down and file away the existing equipment first (so as not to make the figure too bulky). Large differences in the surface (folds of clothing) are also best gotten rid of first.
When the putty is in place, start from a corner and poke a hole there. Then another next to it, but rather than leaving it at that, draw the tool slightly to the previous one. Repeat until an end is reached, or you're round (when sculpting a mail hood for example). Then start at the other end (where your just finished the previous row), and do the next line in the opposite direction. Repeat that many more times, and it should all come together nicely.
Type of tool depends mostly on the ringsize you're looking for. Although I've used them in the past, I would advice against a tool with a tapering point, as thickness of the putty may alter the size of various links in the mail somewhat (more shallow ones being smaller). Personal favourite these these is simply a piece of brass rod filed down, to give a sturdy, thin round end. A pin with the point clipped off is used for characters that deserve even smaller mail, which technically is even more realistic (and very much more time consuming).
Haradrim King with some sculpted chainmail:
And Thranduil, with extra-fine needle-sculpted mail:
