The display of costume in this manner is a complicated beast. Following a talk by the McCord's Chief Conservator, Anne MacKay, it was clear that those involved with the process require a great deal of knowledge about a garment before mounting it. This includes the period in which the garment originated, intended silhouette, method of construction, size and materials. This is important not only for achieving an attractive presentation on a mannequin, but for the long-term preservation of a garment. Mounting it incorrectly ie: a 1920s Flapper dress that has been sewn on the bias with little support on a mannequin can have damaging effects. Mounting correctly, like for instance a corset from the turn of the century, can sometimes help to give shape to a garment that has been lost overtime by sitting flat in museum storage. There are also numerous other considerations including lighting, positioning of the dress stand and length of time exhibited that concern conservators.
The McCord used supplies for building their mannequins similar to those used by a milliner: buckrum, glue, twill tape, wire, nylon boning, hoop steel, stockinette cotton and various other creative materials when required. They recommended buckrum for the main body of the form be black for display purposes to help prevent it from showing in dark exhibition galleries. Also, understructures like petticoats or bustles should be made out of cotton or tulle to create the period silhouette. One supplier which carries many of these materials and that I personally recommend, as I shopped there while a student, is Farthingales in Stratford, Ontario.
I will not get into the "how to's" of construction here, because there are far too many techniques. Below is a list of resources for constructing dress stands that are available online.
Making Mounts from Kent State University Museum:
http://dept.kent.edu/museum/staff/mount.html
A comprehensive bibliography from ARG! Alberta Regional Group of Conservators http://www.cac-accr.ca/english/arg_mann.asp
Image of mannequin from Wiki Commons.