These days it's not hard to find neem toothpaste, neem mouth wash, or tooth powder.
Neem toothpaste usually contains the neem leaf extract only, a mouth wash may contain leaf or bark, or both.
Neem tooth powder can use the bark and/or the seed.
Leaf extract has repeatedly been tested in clinical studies. It is indeed very effective in treating even advanced gum disease and maintaining healthy gums and teeth.
However...
However, in India it's not the leaf that is traditionally used in oral care. The bark is much more effective.
Bark powder achieved the most dramatic results when treating patients with advanced gum disease.
(Read more about studies and research results regarding neem and gum disease.)
If you are growing a neem tree or live in a region where they grow naturally, you can easily prepare your own powder. Collect the bark, dry it, and grind it with a pestle and mortar. Just dip your loaded tooth brush into the powder.
Alternatively you can do what the Indians do and chew on a neem twig every day. It's not particularly tasty, rather bitter, but it works.
You can even make your own neem toothbrush like the Indian people do.
If you don't grow neem yourself you may be able to find neem bark powders online. (Neem bark powder is recommended for people who already have gum problems.)
Or simply start using a good neem toothpaste and mouthwash.
(Both the products I just linked contain both neem leaf and neem bark.)
Oral care is one of the uses of neem that I strongly recommend for anyone.