1
My father teached me how to ride a bike.
My father taught me how to ride a bike.
Teach is an irregular verb. Its past simple and past participle form is taught, not teached: ‘Our teacher taught us a new song.’ ‘She has taught English for ten years.’
2
My teacher taught to us some new words.
My teacher taught us some new words.
My teacher taught some new words to us.
Teach is one of the verbs that can have two objects: a person and a thing.
When the person comes first, do not use to: ‘She taught us English.’
When the thing comes first, use to before the person: ‘She taught English to us.’
See LEARN