On average, I acquire around 1,000 greaters per month and 4,000 lessers per month. The lessers are acquired via deconstruction.
I did a search on the forums and I found a Gathering Ingredients thread but that poster just wanted to know what quests to run to get essences.
I classify myself as a frequent gamer not a power gamer.
After three months of testing on a new server with new characters, I wanted to see how many greaters and lessers I could acquire.
I purchased no essences on the AH as initially I was poor. Plus, it would ruin the test.
I never found a crafting experience elixir as loot.
The first two months I sold the essences for roughly 250,000 plat for the entire lot of lessers and greaters that I had.
My character I designated as the crafter only deconstructed. I never once made a shard. My crafting character is a level 34 in Arcane and level 26 in the other two. All of that was accomplished by deconstruction only.
For those that are new to crafting, It is a major grind. You will need 10s of thousands of essences to get to level 150.
My thoughts now, deconstruct, save essences, and then search for a crafter to craft you what you want from your stash of essences.
Most Common Lesser or Greater = Mind or Body
Rarest Greater to find = Law or Chaos
Rarest Lesser to find = Law or Evil