There are 6 regular Fairy Fountains in Hyrule. They are:

1)Hyrule Field
Once you have the Goron Bracelet and Bomb Bag, there is a Fairy Fountain you can find under a boulder in Hyrule Field near the stream & trees

2)Graveyard
Once you have bombs, bomb the wall behind the treasure chest in the grave where you found the Hylian Shield in the Graveyard.

3)Zora's River
Fly with a chicken onto a thin ledge with a ladder leading up from it. On the top of the ladder there is a boulder surrounded by small rocks. Bomb it to find the 3rd fountain.

4)Lost Woods
In the maze by the Sacred Forest Meadow, there is a ladder up to the top of the maze which leads to a hole that has a Fountain in it.

5)Zora's Domain
On the small island in the water by the waterfall in Zora's Domain, play the Song of Storms to open up a hole and lead you to another fountain.

6)Gerudo Fortress
Play the Song of Storms behind some crates near the large flag in the fortress to open up a hole to the last Fountain.