The basic traditional home remedy remedy for tooth ache was to remove the tooth. Since prehistoric times until just 100 years ago or so, removal was the most common remedy for tooth ache. However, there have always been a number of folk remedies which ease tooth ache.
Oil of cloves can ease pain by deadening the exposed nerves on a cavity. A drop of oil on a wad of clean kitchen towel or lint free cloth can be pushed into the tooth in qiuestion. This rememdy hurts a bit for about the first minute but then the nerve ending stop functioning and the pain goes away completely.
Ice placed directly on a throbbing tooth will also ease the pain to some extent. This is a better option than oil of cloves for younger children.
A wad of cotton wool soaked in brandy can be squeezed against a cavity to numb the pain of toothache. This is how my mother dealt with toothache such as the pain of new teeth breaking through in our family.
Oil of oregano is also favoured for pain relief on an aching tooth. I read this one in a folk remedy book but have never tested its effectiveness myself.
A salt water mouthwash is an effective cure for mouth ulcers. It can also help clear away a small infection if that is the cause of the toothache. This is always a sensible option for all children and adults with toothache. In fact, my dentist actively reccomends it as a safe and effective remedy. Younger children should be carefully supervised to ensure they don't swallow the salt water when swooshing it around their teeth.
The basic truth is that teeth hurt when nerves get exposed indicating inflammation and possibly some infection. This almosts always means ultimately you will need to visit your dentist. Therefore, regular brushing, flossing and good oral hygene are the best long term preventative cures for toothache.