For both business and evening events, the double-breasted suit lends a debonair look to the wearer. While the single-breasted suit has its origins in equestrian activities, the double-breasted suit finds its stylistic roots in military attire. Traditional military suits often feature six-by-six or even eight-by-eight buttons and have an extremely high button point, showing off two parallel rows of buttons flowing down the torso. The preciseness of the two rows emphasizes military precision and order.
As such, the double-breasted suit is considered to be more formal. One should never fully unbutton a double-breasted suit while standing or sitting because this creates a sloppy look that is at odds with the formality of the suit. 
In general, the middle right button should always be kept buttoned, while the lower right button can be left unbuttoned to subtly mitigate some of the suit’s formality.
Indeed, the double-breasted suit, while formal, is still amenable to personal touches of flair. The Duke of Kent started the trend of leaving the top right button of his six-by-four unfastened, but fastening the bottom right button. This practice, now aptly known as the Kent style, was adopted and popularized by Prince Edward, the Duke of Windsor. The always elegant Fred Astaire even leaves the inner left button unfastened to create his favored dégagé style.
To pull off this look, the coat needs to be cut specifically for the top button to "roll over" to the bottom one. Similar to the effect created by the three-roll-to-two in a single-breasted coat, a longer lapel line is created, giving the illusion of a taller, leaner look perfect for wider men. Despite this, I would personally recommend fastening the top right button when one is sitting down to prevent the lapels from gaping "open".
Should you want to, you can choose to wear your double-breasted suit with a waistcoat underneath. However, the waistcoat should be single-breasted and never double-breasted. And it has to be cut in such a way that its lapel line echoes that of the main coat and just peeks out, no more than three-quarters of an inch above the crossover point. As a point of interest, a single-breasted suit can be matched with either a single- or double-breasted waistcoat.
Vents are slits cut into the bottom edges of a coat to allow freedom of movement for the wearer, but they are optional. The double-breasted suit is normally made without a center vent. This is the preserve of the equestrian-derived single-breasted suit. An unvented double-breasted coat emphasizes the V shape created by the lapels and is generally preferred, though a double-vented coat looks equally elegant.