Esseles is the first flashpoint you hit as the Republic. To get to it, go to the Fleet. If you're already at the Fleet, go to the southern elevator -- Coruscant Departures -- and look for the questgiver.
Esseles is a 2-player flashpoint, but you can bring 4. There's not much needed in terms of tanking nor healing, although if you know those concepts, it doesn't hurt. Mostly, a tactic of "GET 'EM!!" works fine.
Note that Esseles is long: about 40 minutes. You can shorten it by skipping all the dialogue by hitting spacebar repeatedly until you get a conversation choice, quickly select an option, and go back to madly tapping the spacebar.
Since these are spoilers, I'll put them in white text, so you'll need to highlight the following to read the boss notes, not that there's much to say.
When you fight the Mandalorian on the Republic ship, he sometimes puts fire on the ground -- you'll see the targeting circles. Just move out.
Just before you get to the giant robot boss on the Imperial ship, you need to flip switches on opposite sides of him simultaneously. Don't get knocked off his platform when fighting him.
The final boss on the Imperial ship, as I recall, doesn't have much special going on. Here's where having an actual tank and an actual healer is nice, but I doubt it's strictly necessary, given that it's the intro instance.