The correct solution for standing water depends on the cause. Standing surface water is caused by a combination of problems. First you don't have any surface grade (flat terrain). The water is on the surface due to impermeable soils or high water table or both. If the problem is impermeable soils in combination with the grade, then your dry well will work. If the problem is due to high water table or saturated ground, then you must correct the grade by digging culverts, tile drains or surface grading.
To determine if a dry well will work, simply dig a hole 3' deep. If it fills with water and becomes a pond, the drywell won't work. If it allow water to drain below a hardpan layer, then expand the hole, fill with course gravel or rock and cover it over. You will need to use drain tiles to collect water around the yard.
If the dry well does not work, you need to determine what direction is going to be downhill and either add soil to raise the grade to promote surface drainage, or excavate a series of shallow tile drains to carry water to the lowest point of your property. If there is no grade or logical drain point you can use a modified dry-well, think sump pit. Install a pump and eject water to the street or roadside ditch.