The most popular invitation set up is a flat 5x7 inch card, with an smaller rsvp card, and extra then sometimes more cards to include maps, directions, reception information, and more.
In the case of a trifold invitation, you can have some of this extra information -maps, directions, and such- printed on the fold(s), though of course the rsvp card is still separate. Below are two examples.
The first example is a card that is about 5x10 inches when unfolded, 5x7 when folded. The main panel is 5x7 inches, with two panels on each side that are approximately 2.5x7 inches. A barn door photograph is printed on the outside of the invitation.
The second example is a card that is also about 5x10 inches when unfolded, 5x7 inches when folded. The main panel is also 5x7 inches. In this case, however, you have a 1.5x7 inch fold on the left, and a 3.5x7 inch panel on the right. The outside is printed with stripes and stylized flowers. This example is made of cream card stock.
Trifold invitations need to be held closed. The easiest way to do that is just to use a small sticker. You can of course use various sizes of stickers. You could also work on a DIY project, closing the invitations with ribbons or bows or whatever else you could think of.
As with all invitations, if you have me design a tri-fold invitation for you, you can change things up a bit. The customer who ordered the barn door invitations went with brown envelopes, for example, instead of white envelopes. Different card stock colors... different designs... different fonts... different colors...
Trifold invitations will cost you more than flat, non-folding invitations. They would cost less than a pocketfold, however, and certainly cost less to mail out than a pocketfold invitation would.
October 9th, 2012 UPDATE:Check out an updated photograph of the barndoor invitation idea: