Kimonos have specific undergarments that produce a layered look, and each piece of underwear has a role. In addition to improving the aesthetic of your kimono, they also help keep it clean from sweat and debris, and they can be washed much more easily than the kimono can. To properly wear a full set of kimono undergarments, you need a "juban" (undershirt), "susoyoke" (skirt), "koshi himo" (a tying cord), and "eri sugata" (under-collar).
Susoyoke are lower body undergarments meant to wrap around the hips as a skirt. They have strings in their upper two corners to tie them in place. To wear a susoyoke, start by centering it against your back like a towel. Then, wrap both corners across each other and around to your back. Tug them slightly upwards as you pull, then tie the strings slightly below the top edge of the skirt. Adding this extra fabric above the strings creates a waistband out of the skirt fabric.
Note that it doesn't matter which side of the susoyoke is wrapped over the other, but you might want to wrap it left-over-right to encourage good kimono-wearing habits.
The juban, a robe-like undershirt, wraps like a kimono. Put it on, and then wrap it about your torso with its left side over its right side. Tie it with two koshi himo a few inches apart, about where an obi would go. A date jime can help secure it as well if you prefer.
The Eri Sugata
Eri sugata are white under-collars that will protect your kimono from sweat or makeup on your neck as well as making your kimono look more layered. They have a fold or slit that sits around the juban's collar; simply insert the juban collar and arrange the eri sugata as you want it to look under your kimono top. In the past, under-collars were sewn to the undergarments, but that is not necessary with modern eri sugata.
Should I Wear A Bra?
In short, no! Kimono are extremely supportive, and they're also meant to not emphasize the breasts. The juban will shield you from any roughness from the kimono proper. If you must wear a bra, wear a sports bra or other compressing garment under your juban. The ideal shape for a body wearing a kimono is a cylinder, like the shape of the kimono itself. Any bras that lift your breasts will cause the kimono to sit poorly.
What About Panties?
Wear panties if you prefer them. Traditionally, susoyoke were worn without anything underneath, but panties will cause no problem for the kimono if you wear them.