There are three different types of customized arrows that you can obtain as adult Link after you have obtained the Fairy Bow from the Forest Temple. It should be noted though that none of the custom arrows are required to complete the game.
The Fire Arrows can be obtained at Lake Hylia after Link has completed the Forest Temple and obtained the Fairy Bow.
You can technically obtain the Fire Arrows as soon as you have the Longshot in your possession, part way through completing the Water Temple, but there is no reason to obtain them until after you fully completed the Temple. It should be noted though that you can use th Scarecrow’s Song to call forth Pierre the Scarecrow and using the Longshot to reach the island in the center of Lake Hylia.
Use the Sun’s Song to change the time to morning. Stand on the brown platform near the Lake Hylia warp point and aim your Fairy Bow over the island off in the distance and towards the sun. Shoot an arrow at the sun as it comes over the tree line. This will cause the Fire Arrow to drop down onto the island. You can now swim over to obtain them (or use the Scarecrow Song if you have not completed the Water Temple but do have the Longshot).
Fire Arrows can be used in place of torches to light things on fire with ease. You can also use it to replace Din's Fire at times in the game but, as mentioned above, you do not need to obtain the Fire Arrows to complete the game.
Check out the Gerudo Training Grounds section for more information about how to obtain the Ice Arrows.
Link automatically obtains the Light Arrows during his meeting with Princess Zelda at the Temple of Time after completing all of the Temples.