In a nutshell, health and nutritional factors are quite easy. If you are healthy, your nails will be healthy. Very few supplements work straight to the nails. They become effective when one is deficient in certain supplements or trace minerals and in turn, may help the nail development.
The old theory that nails need calcium, thus to improve your nails you should drink milk or take calcium supplements. Nails have almost no calcium in their composition so taking calcium supplements will not help them grow faster. Nails are formed mostly from keratin, a protein, which can be derived from diet.
How about the "drink gelatin every day" to combat brittle nails? This has been suggested for many decades, back to Grandma's time, with very little evidence to support that claim. Perhaps back then, during trying economic times, gelatin was an inexpensive source of protein so it may have improved nail health for those whose diet was lacking in balance and protein. Today, it is no longer necessary for nail health as a supplement.
There is, however, one B-complex vitamin that has shown to improve nail firmness, hardness and thickness. Biotin. Many "all encompassing" supplements include Biotin in the formula and market them to improve "nails, skin and hair". The amount of Biotin in these products is minimal and greater results may be seen by taking a daily dose of 2500 mcg plain Biotin. Check with your doctor prior to taking any supplements.
As with anything concerning our health, many factors contribute to our overall physical condition and our fingernails and toenails are usually a good indicator.
If you are experiencing problem nails, consult with your health care or nutritional professional to discover if you might have any deficiencies that would contribute to weak, brittle nails.