1 How do you dare talk to him? (modal)
2 How do you dare to talk to him. (lexical)
The difference is clear. However, there are blended uses like
3 She dares not say a word.
4 I dare you kiss that girl.
As far as I know 3 and 4 are grammatically correct. Do you agree with it? What's the difference between
3 She dares not say a word. and She dare not say a word
4 I dare you kiss that girl. and I dare you to kiss that girl.
The modal form is not a matter of the presence of "to" but whether "do support" is used:
How dare you talk to him! (modal, rhetorical, figurative)
How do you dare (to) talk to him? (lexical, question, non-figurative)
The lexical verb dare can take either a bare infinitive or a to-infinitive
He dares/dared to swim with crocodiles / He dares/dared swim with crocodiles
These are both lexical, as indicate by the fact that they take regular past tense and third person singular. The modal form would be "He dare swim with crocodiles" This would be rare in modern English.
The forms you have in 3,4 would be interpreted as lexical,
In three the lexical form "She dares" is favoured as the modal form is now dated or archaic.
In 4 the preferred form be "I dare you to kiss the girl". As this is a specific real challenge, a "dare", rather than being a mode of the verb "kiss".
