Header image: "Celestial dancer (Devata)." Central India, Madhya Pradesh; mid-11th century A.D. Courtesy of the Met Museum.
Simply put: They're not split skirts. Pulp-novel and comics illustrators get this one wrong all the time, usually in regard to the simplest form of loincloth, the breechclout or breechcloth.
The breechclout is a very simple garment, and it can take up about as little or as much material as is practical in a given culture. The defining characteristic is a piece of material pressed front-to-back (or back-to-front) against the wearer's genitals, held up by ties or a belt, and without wrappings for the legs. If there's not much material left over, then there's no confusion: It's more or less a tie-on panty. If, however, there's excess material at the front or the back, then that excess forms an apron which covers the material on the crotch, leaving people to assume it isn't there.
Some ways to wear a breechclout:
Sew tapes or a sash to one end of a long piece of cloth (or hide, if you prefer and have access to it). Tie the tapes in front or back of your body, with the clout hanging down on your opposite side. Pull the clout between the legs, over the tie, and let the clout fall to make an apron in front.
Situate the clout between your legs and hold the excess length up, then fasten a belt around your waist with equal lengths of fabric spilling over it in front in back, and let go of the aprons.
If you're good with the panty look, add tapes to all four corners of the clout. Stand over the clout, lift it to your crotch, and tie the tapes.
You sometimes see more complex loincloths in cultures with large looms and soft fibers for spinning/weaving. Wearers of the Japanese fundoshi skip the belt, instead wrapping the fabric repeatedly around the waist (as well as under the genitals) before tucking in one or both ends; Aztec paintings seem to show a similar technique. The Indian dhoti is voluminous enough for the excess to wrap each leg, as well as often containing pleats. Westerns will likely recognize the ancient Greek perizoma, a beltless, knotted style shorter than the dhoti but more modest than fundoshi, from Christian religious art, as artists traditionally depict Jesus wearing it on the cross.
One item of debatable construction is the ancient Egyptian shendyt, or schenti (center top). I have yet to see any signs of an end tucked into the back; meanwhile, the front apron can appear either on top of or below the side flaps (right). Some examples clearly have a separate belt; others seem to be secured by wrapping of the fabric around the waist (as with fundoshi) or by hidden tapes.
Tutankhamun's grave goods offer 145 examples of the latter kind. His many loincloths consisted of linen isosceles triangles with tapes. The triangular shape accounts for the wide hip coverage typical of the shendyt, but otherwise would have made a typical breechclout with a front apron on top, using the first technique from the above list. However, it does not account for the variation that we see in placement of the front apron. If anyone knows of an extant example of a loincloth designed to produce the effect of side flaps overlapping the front apron, please let me know where to find it so that I can add it to this site.
recommended resources
How to Put on a Loincloth, at WikiHow, offers step-by-step instructions for dressing in a waist-wrapped style.
Forgotten Riches of King Tut, by The New York Times, includes a description of Tutankhamun's underwear by one of the first researchers to analyze it.
Breechcloth/Breechclout and Leggings, from native-languages.org, has some dead links, but still features clear (and SFW) diagrams of North American Native styles.