Speckled Tastyfish can only be fished from a 'School of Tastyfish', which spawn along the coast of Stranglethorn Vale, but only during the two hours of the event, and never in Booty Bay.
Schools of Tastyfish are a kind of Fishing pool and look like churning circles of fish. Your tooltip will say "School of Tastyfish" when your mouse points to one.
When the event starts, travel up and down the coast, looking for a School of Tasty Fish.
With your fishing pole equipped, face the school and cast.
Your bobber must land inside the school in order to catch the event fish, so cast again each time the bobber lands outside of the circle.
Once a certain number of Tastyfish have been caught from a school (3 or 4), the school will scatter and you'll need to find another School of Tasty Fish.
When you have caught 40 Speckled Tastyfish, turn them in immediately.
At one time a skill of 130 was required to catch anything other than trash from the Schools of Tastyfish, but in patch 3.3 this changed. At the present, any successful catch, i.e. anything other than No Fish Were Hooked, from a pool will result in catching what that pool contains. This means that anyone with a fishing skill of 1 can, theoretically, win the Extravaganza.
A skill of at least 100 is highly recommended, however, so that you may learn Find Fish. With the [Find Fish] ability, Schools of Tastyfish will appear on your minimap. Try to acquire a [Weather-Beaten Journal] and learn the ability prior to the event. They can be found in trunks and chests fished from any school in Kalimdor or the Eastern Kingoms. Junk pools drop chests more often than fish pools, so these are a better source for the book if you are farming it.
Practice fishing Fishing pools prior to your first Stranglethorn Fishing Extravaganza, so you know how the placement of the bobber in the circle works.
Set your [Hearthstone] to the Booty Bay inn to expedite your turn-in.
Bring assistance. Take turns on who assists/competes in a given week (but don't switch roles within a week during the competition.)
Friends can spot spawning Schools for you.
Stranglethorn Vale has level 31-40 mobs. Friends can help with this if you need help.
You can deplete 'their' School of Tastyfish by fishing it.
On a PvP server, the Stranglethorn Fishing Extravaganza is essentially a battleground. Ganking is a valid contest strategy. Come with many friends.