The Wikipedia entry on die proof is all but worthless for US material. It disseminates misinformation that is not reliable.
The Linns item is much more useful and reliable, but without illustration. Nonetheless, the information about proofs it gives for US material corresponds in the main with what essay-proof specialists have been saying for many years.
One point that may need to be updated is the note that proofs of recent issues are all but unobtainable. I was recently told by an informant "in the trade" that in view of its fiscal difficulties, the USPS is considering making some of its contemporary proofs available for collectors. No program for this has been announced or started as of yet, but this is a development in the works. Stay tuned.
As to your initial question:
Contrary to the Wikipedia item, India paper is a thin, opaque paper made especially from bamboo fibers and with very little sizing agent in it. As a result it is a limp, fragile paper that is easily damaged, but conforms well to the contours of an engraved image and so makes superior proofs. To do that, the die or plate is inked and wiped, then a sheet of slightly moistened India paper is placed over the die or plate, completely covering it, which was sometimes lightly dusted with a very fine powder like cornstarch. Over this a sheet of very white cardstock is placed to support the India paper during printing, and the whole stack is fed into the proving press, which was usually a manual spider press. The pressure of the press would cause the India to bond to the cardstock, and the unprinted outline of the die or plate would be pressed into the card as well. The area where that outer impression is made is called the
sinkage, which of course includes the entire area of printing.
Die and plate proofs are sometimes "pulled" (aka printed) directly on cardstock, either as presentation items, or when color is the primary point of interest. It is lightly moistened and then placed over the die or plate and run into the proving press.
Here is a link to a demonstration of the process by a BEP technician.
http://www.youtube.com/watch?v=DDTuIu8PWkw br / He uses a soft wove paper that is more rigid than India and no backing card, but otherwise it is the same process.