I read the following home remedy in a book - The complete Book of Ayurvedic Home Remedies.
" Take some sesame oil and throw neem leaf mixture into it. Heat this mixture until all the moisture evaporates - may take a couple of hours. Now use this Neem extract of Sesame on the scalp. This will take care of the dandruff."
Since the book talks about allowing the moisture to evaporate, I believe that it recommends taking some fresh leaves along with a little water and making a paste of it in a blender. And then mixing this with the oil and heating on medium to low heat, allowing the water to distill off leaving the neem extracts in the oil.
But this is too much work. It is easier to buy a pack of dry neem leaf powder and soak it it water and then apply the paste on the scalp. Other Ayurvedic herbs used for beautiful hair are Shikakai, amla and aritha. Soak these powders in water overnight, and apply the next day to the scalp, and then wash with warm water after a couple of hours. Do not use synthetic shampoo or conditioners. Drinking a herbal tea made of cumin, fennel and coriander seeds also helps alleviate the pitta which is the root cause of Acne and dandruff.