Bamboo have two main types of root systems - running, and clumping.
From the photo, it looks like you have a clumping bamboo - which is GREAT - because it won't try to take over your hard.
Dig down until you can see the root system. Clumpers expand by a rhizome that has a thin neck where it leaves the parent plant. Like Jerry says, the outside edge of the rhizome is bulbous, and will have a beard of roots.
Cut at the narrow neck where it joins the parent plant.
If your soil allows, take some dirt with the beard. The health of the roots has a great deal to do with whether it survives the transplant. So its better to disturb them as little as you can.
Treat it like you would grass - miracle grow is great.
As tall as your bamboo is - fish pole bamboo? - cut the top off, too. The roots will need to grow to support that tall top. Leave at least one branching node - where the branches come off the main trunk and already have leaves.
