It was best used by DPS champions that would benefit from high attack speed and/or crit chance, like Tryndamere. It was most often bought late game because the crit chance stat needed other late game crit items to be effective.
Elixirs are often bought towards the end of long games when builds are all completed and the extra gold continues to accumulate. They can also be bought mid game to give a temporary stat advantage during ganks and teamfights.
Elixirs are automatically applied when purchased if there are already 6 items in the inventory.