You're getting lots of good advice.
I just wanted to make a point. I don't know what kind of digging tools you have but using a good tool makes a world of difference.
If you can't afford anything expensive you you can go to Home Depot (or elsewhere) and buy a tool. I paid ten bucks for an Ames digging tool which is basically identical to the Fiskar's digging tool that you can look at Here:
Fiskars Big Grip Multi-Purpose Planting Tool: Gardening & Lawn Care : Walmart.com
They have a smooth blade side and a VERY sharp saw blade side that slices through roots like butter. They cut a nice clean plug. My holes are SO much better now. I started off using a folding US army trench shovel (which is still awesome for rocks, some roots and deeper digging) and a regular gardening trowel.
The Fiskar's tools can get a bit pricy but they're great.
The Hori Tori tools are good too and inexpensive as well. Just get whatever feels right for you and fits your budget. Everyone has their own personal preferences, likes and dislikes.
Also, a big plug is a good thing sometimes. if you dig too small a plug you end up having to make the hole bigger and your original plug no longer fills the hole and you end up with a messy looking hole when you're done. Make sure you dig your plug at least a little bigger than your target so you can pop it right back where it goes nice and snug.
Also, don't dig down on an angle. Go STRAIGHT down, all they way around your "C". That way when you replace the plug. it's far less likely to come back out of the hole.
Remember, like any skill in life, practice makes perfect. The more you dig the better you'll get at it.
I hope this helps and HH.