How do i unclog my back yard sewer drain?

Depends on the system - if it is connected to a municipal or storm sewer, you would clean it out with a snake to the main - and this may have to be done professionally. If it is a French-Drain type system, there is no practical way to clean it as when it fills up it relies on natural drainage into the soil to empty. And if the ground is saturated - that may take a good deal of time.