Beans, dark leafy greens, fruits especially high in Vitamin C, nuts especially Brazil nuts (you only need 1 a day to get the daily requirements of selenium,) salmon which helps hydrates your skin and strengthens your nails, adds strength to your hair and improves the shine of your hair.
Foods that are bad: sugar. When your blood sugar rises due to eating sweets, the body produces insulin in response. This raises the levels of androgen, which is a male hormone, then shrinks the hair follicle in both women and men. Therefore, foods that are starchy and made with white flour will do the same. They are quickly broken down into sugars and pose the same problems. Too much vitamin A can lead to hair loss. A typical multivitamin won't contain too much. Beta carotene is a safer way of getting that Vitamin A.
Skin, hair and nails all need protein to grow. Many people don't get enough in their diets. Protein isn't just found in meat. Beans, tofu, spinach, lentils all contain protein. If you have a bean dish and serve it with rice, (brown rice being more nutritious and healthy than white rice,) you will have a complete protein.
Foods that contain an amino acid called cystine, which creates keratin is also beneficial. Food like pork, broccoli, Brussel sprouts, garlic, onions, whats and red peppers fall in this category.
Not enough iron or zinc can lead to hair, skin and nail issues. If you see white spots on your nails, it could be an indication that you are not getting enough zinc. Zinc and iron are essential to keratin formation. Beans are often a good source of each. (Don't confuse those white spots with the ones you get from bumping your fingernails.)
Biotin is often recommended as a dietary supplement for strengthening hair and nails, though scientific data supporting this usage are weak. Nevertheless, biotin is found in many cosmetics and health products for the hair and skin. Foods with a relatively high biotin content include Swiss chard, liver, leafy green vegetables, and peanuts. Other foods containing biotin are cauliflower, salmon, carrots, bananas, soy flour, cereals, and yeast. Biotin content of food is reduced by cooking and preserving.
These are just a few suggestions to get you started on the road to more beautiful hair, skin and nails. Best to you.