If you say that you would sooner do something or you'd sooner do it, you mean that you would prefer to do it.
Ford vowed that he would sooner burn his factory to the ground than build a singlevehicle for war purposes.
I'd sooner not talk about it.
I'd sooner he didn't know till I've talked to Pete.
I would sooner give up sleep than miss my evening class.
I'd sooner not, if you don't mind. [MODAL not]