Q.I have a garden that is very wet. One area is like a puddle. If I put peony plant in that area will this help with drainage?
How can I drain some of the water in my garden

Plants generally will not help with soil drainage.
Amending the soil or making changes to the landscape so that soil drains properly is the changes that you most likely need to make.
These articles will help you get started.
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/avoiding-wet-soil-tilling.htm
https://www.gardeningknowhow.com/ornamental/water-plants/wgen/water-tolerant-plants.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/yard-drainage-problems.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/making-sure-soil-drains-well.htm