Pepper plants, unlike tomatoes and some other vegetables are generally pretty sturdy, but they have been known to break on occasion. Staking pepper plants does have its advantages. It lends support to the plant - maintaining an upright position with proper supports will keep the peppers from dragging the plant down, thus keeping them off the ground where they are vulnerable to insects and disease. Staking can also help prevent sun-scald.
The simplest and probably the most efficient way to stake pepper plants is to drive the stake into the ground directly next to the plant - not so close where you're going to mutilate the roots when you drive it, but within an inch or two of the main stem. Then, tie the main stem and branches of the plant to the stake fairly loose.
I like to use pantyhose or old nylon stockings - some people use shredded sheets etcetra.