Dindrenzi seem pretty easy to start; point and shoot, but there is a lot more to the fleet. Dindrenzi don't have more firepower than other factions, but they can potentially use that firepower FIRST. I've had games where my opponent's played into my hands, and I was able to systematically destroy their fleet with few losses. I've also had games where my opponent out-maneuvered me, effectively blocked shots with terrain, and tore me to pieces with a ton of weak shots (Aquans are particularly adept at this).
I can sum up the Dindrenzi play style with a simple motto: Strike Hard, Strike Fast, GTFO!
Basically, you want to be shooting stuff with your Rail Cannons Turn 1. Compared to everyone else, Dindrenzi can cause damage from 48" away, and it's important to inflict this damage. It's also important to keep this distance open for as long as possible, and to not rush to that juicy RB2 at 24". Ideally, your entire fleet will be able to hit RB2 on your terms, on your turn.
Once you have gotten that 24" shot off, it's time to think about starting a Fold Space escape. While you might be able to get a second RB2 shot off with a squadron, it also puts you in range of their best weapon ranges, and with stock DR and no special defenses, your ships can very quickly evaporate. I'm still learning when is the right time to leave. Basically, if you are dropping a Mine and expecting to do damage with it, it's definately time to leave; maybe past time.
For fighting Aquans, it's really important to swing for the fence and always roll as many dice as possible. With Shields, Difficult Target, and a boosted DR, Aquans can be very hard to damage. However, their CR tends to be low, so getting a Critical Hit must be your goal. If you're lucky, you might get a bunch of 6s and double-Crit Kill one of their OP Cruisers. (I think Aquan Cruisers are the most OP unit in the game; your friends will probably argue very strongly against it, while always taking 4 or 8 of them)
Dindrenzi Frigates are your friend against Aquans. They ignore Difficult Target and Elusive, and can roll up to 12 AD and 8AD of Torpedoes at 24". Used correctly, they can be decisive in your games.