Leather is a natural product and porous material. As such, it is subject to change from one piece to another throughout its life-time and with daily use. This is very normal and expected to occur. Expect it to evolve with you.
Due to certain tanning processes, some color transfer may occur and this too is normal. Leather is not waterproof, though a splash of water here and there should not hurt it. However, water spotting may occur if exposed to rain/water. All care should be taken to avoid contact with excessive sweat, water, perfumes or dirt to prevent unwanted discoloration and/or damage.
For natural undyed vegetable tanned leather:
If you wish to accelerate the aging and darkening process of this leather, you may want to apply a few light coats of Neatsfoot oil/mink oil/ leather conditioner and let it dry for a few hours. At first, the leather will look much darker and may show streaks from the application, but as the oil dries, the tones will settle and lighten up a bit. To darken it more, you can sit the item in the sun for a few hours. You’ll notice it start to darken just like skin does. Depending on the time of year and intensity of the sun’s rays, this may take a few hours or a few days to darken. Remember, your leather item will evolve with you and will continue to darken the more you handle it and expose it to the oils of your hands, exposure to indigo and dirt, sun, water, etc. That’s all part of the beauty and appeal of this kind of leather.
For suede leather:
Suede is very delicate. To remove lint, dust and dirt from your strap, use a soft and clean brush/toothbrush and lightly brush over the surface of the strap to remove debris. Do not expose to water, excessive sweat or perfumes as stains from these cannot be removed from suede. Lightly spray with a suede protector to help keep it from getting too dirty.
For vegetable tanned, oil tanned, and others leather:
If you find that your leather item is starting to look dirty you may want to take a mildly damp sponge or clean t-shirt and use a tiny quantity of a product like saddle soap to clean it. Let it dry and remember to apply leather conditioner afterwards to replace the moisture it lost when it was being cleaned. Remember that some conditioners darken leather more than others, so make sure to test in an inconspicuous spot before applying to the entire item. As important as it is to keep leather conditioned, take care in not over conditioning as this weakens the fibers and can also cause mildew to grow. So apply generously but without over-doing it.
Leather is not waterproof, though a splash of water here and there should not hurt it. If you plan on getting your strap wet regularly, you can look for straps made by waterproof materials, such as canvas, oil tanned, or other water-resistant materials. Besides, you can also use a leather lotion or oil to maintain the oils of the leather. Be sure to spot test on the back of the strap to see how the lotion will effect the color of the strap. It usually darkens it.