First of all, using the correct digging tool is essential. I use a Lesche relic shovel when I am wooded areas, but in a school yard I would use a small trowel.
I always try to dig deeper than my target reading, for example if I get a coin at 6 inches I will dig a cone shaped plug approximately 10 inches deep. If the area allows it, I usually make my plugs about the same circumference as the coil. This prevents accidental "stabbing" of valuable targets. When detecting in grass, I only cut 3/4 of the way around. This allows the grass to grow back in quickly.
If it is a manicured lawn, I will flip the plug onto a towel in order to capture all the dirt.
I hope this helps.
Neil