Hi Lily,
It depends on how old the root structure is. If your peony was potted you might get blooms this year, but don't expect them. It could take a couple of years before it blooms. If your peony roots were just dug up they might not bloom for another 3 years. The most important thing to keep in mind when planting them is to make sure that the 'eyes' (sprouts) aren't planted any deeper then 1 1/2" below the soil. Here's a site all about peonies. I suspect that yours is herbaceous.
http://www.goldenport.com/peony/index.htm
Newt
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.