How do I stop backyard from flooding when it rains hard?
Put in one of these. It's a French Drain, it is also on this sites FAQ.
How do I build a French drain?

The need for a French Drain arises from a few problems, but usually from standing water in or around your home. This is caused by poor drainage, usually from clay rich soil or overly compacted soil. A French Drain will relocate the water very efficently. Link tot he question above for specifics.