How do I get Souls?

Soul of Flight: Wyvern
Soul of Fright: Skeletron Prime, Hardmode Skeletron
Soul of Light: Hallowed enemies (Illuminated Slime, etc)
Soul of Might: Destroyer, Hardmode Eater of Worlds
Soul of Night: Corrupted enemies (Green Jellyfish, Eater of Souls, etc.)
Soul of Sight: The Twins (Spazmatism and Retinazer) Hardmode Eye of Cthulu

Crafting recipes for the mechanical summoning totems are easliy gotten from The Guide by showing him Iron or Copper bars.

It should also be noted that in order for these monsters to appear, one must first defeat the Wall of Flesh.

The Souls items do not need any sort of item to extract them from monsters. They are drops from specific Hard Mode enemies.

Once you have defeated the Wall of Flesh and entered Hard Mode, you can get those souls from the following enemies:

+----------------+-------------------------------------------------+-----------------------------------------------------------------------------------+
|   Soul Name    |                      Enemy                      |                                  Enemy Location                                   |
+----------------+-------------------------------------------------+-----------------------------------------------------------------------------------+
| Soul of Night  | Any enemy in the Underground Corruption/Crimson | Underground Corruption/Crimson                                                    |
| Soul of Light  | Any enemy in the Underground Hallow             | Underground Hallow                                                                |
| Soul of Flight | Wyvern                                          | High Altitudes (Look for harpies)                                                 |
| Soul of Might  | The Destroyer                                   | Use a Mechanical Worm at night                                                    |
| Soul of Sight  | The Twins                                       | Use a Mechanical Eye at night                                                     |
| Soul of Fright | Skeletron Prime                                 | Use a Mechanical Skull at night                                                   |
+----------------+-------------------------------------------------+-----------------------------------------------------------------------------------+

For each of the bosses, there is also a chance each night that they will spawn on their own (similar to the Eye of Cthulu).

For the Souls of Night and Light, note that it does not have to be an enemy from that biome. Any enemy that dies in that the appropriate corrupted biome has a chance to drop a soul. For example, if I have Underground Hallow and underground Corruption biomes right next to each other and I lure an enemy from the Hallow into the Corruption, it has a chance to drop a Soul of Night.