《can》
She can swim.
↓
Can she swim?
彼女は泳げますか。
※ 丁寧な表現→ Could she swim?
↓
Yes, she can./No, she can't.
《will》
You will come to the party.
↓
Will you come to the party?
パーティーに来ますか。
※ 丁寧な表現→ Would you come to the party?
↓
Yes, I will./No, I will not [won't].
《may》
I may open a window.
↓
May I open a window?
窓を開けてもいいですか。
※ 丁寧な表現→ Might I open a window?
↓
Yes, you can./No, you can't.
《shall》
I shall help you.
↓
Shall I help you?
手伝いましょうか。
※ 丁寧な表現→ Should I help you?
↓
Yes, please./No, thank you.