To be frank, there is no 'right' way to cut toenails. Every person has their own individual taste for how long they would like their nails to be- a sort of 'comfort zone'. Nails can be whatever reasonable length you feel comfortable with. However, keep in mind that excessively long nails can irritate the skin to the toe next to the nail, and are also at greater risk for being pulled off in an injury. Additionally, nails that are cut too short can place the skin directly under the nail at greater risk for injury during the nail cutting itself.
It is also a common myth that the way you cut your nails has an effect on how the nail grows. The nail grows from a group of cells under the skin at the base of the nail called the nail matrix. These cells are not influenced by the shape of the nail at the end. You cannot 'cause' an ingrown nail to form by cutting the nail a certain way. However, if you cut the nail too closely along the nail corner and 'nip' a little of the skin next to the nail, the skin can become inflamed, and an already existing ingrown toenail that was previously painless can become painful as the inflamed skin presses into the nail. For this reason, probably the single best way to cut a toenail is simply straight across, to avoid irritating the skin.
Cutting the nail straight across is of great importance if you are diabetic, have poor circulation to your feet, or have poor sensation (peripheral neuropathy) outside of diabetes. Skin injuries during the trimming of your own nails can have serious consequences, such as sores and infections. Some diabetics have lost toes to amputations due to infections from self-inflicted injuries after trimming their own nails. In fact, we strongly recommend that if you are a diabetic with poor foot sensation, have peripheral neuropathy of another cause, or have poor blood flow to your feet, you should let our staff care for your nails for the sake of safety.
One final consideration is the use of an appropriate instrument for cutting your nails. A traditional nail cutter uses a lever-like mechanism to chop the nail. This works fine for nails of normal thickness, but the jaws of the cutter do not open wide enough to accommodate for thicker nails. In the case of thicker toenails, a side cutting nail nipper (similar in appearance to wire cutters in a tool box) is a better choice. However, the sharp tips of the nipper jaws can cause harm to the skin if you are not careful and accurate.