1.) One Power Berry is located underneath your farm, it is in a random spot and may only be dug up using the hoe (you must plow the ground one spot at a time, or it will not appear).
2.) Another Power Berry is found on the third floor of the mine, its hard to get, but you eventually should get it.
3.) You can win this one at the first Egg Festival.
4.) You purchase this Power Berry for 1000 gold at the first Flower Festival.
5.) Catch a Large Fish, then throw it into the Pond behind the Fishermen's Tent.
6.) In the winter smash the large rock on the pond behind the fishermen's tent using the fully upgraded hammer.
7.) Buy both Pink Cat Mint and Moon Drop flowers, plant a lot of them at your farm, and then wait till there fully grown, Kents, the small black haired kid should arrive and trade you some marbles for a flower, then give these marbles to the harvest elves in the mountain.
8.) Throw a Vegetable in the pond behind the Carpenter and ask for Strength from the Goddess (You cannot do any work for that day or else you will not receive the power berry.
9.) Be very nice to the Botanist and he will come by your farm to give one to you.
10.) Fish at the Beach often, over time you will catch a Power Berry