Not sure what difficulty you are playing on but I've been playing on Gifted and winning pretty frequently, and I wouldn't consider myself a great strategy gamer. Try watching some of Macsen LP's Let's Plays on YouTube. . . they are extremely helpful. Here's my main recommendations:
1) You MUST do well during the colonization stage in the beginning and totally focus on getting as many good planets as you can. If you don't do this part well, you have no chance. You should be 100% focused on the beginning in just getting a colony ship to planets and claiming them.
2) You must pick the right ideology items early on so that you can reap the benefits later in the game.
3) Negotiate open borders and research diplomacy early on to keep you out of war
4) Set your "govern" triangle at 40/40/20 (20 being money) and just leave it there. Honestly the economy system in the game is pretty much broken in my opinion. . . you just leave it there, try to not "rush" buy too many things, and "re-up" at the "minor race bank" when you run out.
5) Trade with minor races for cold, hard cash to keep your economy going
6) Later, cause mayhem by trading with various factions to go to war with each other, particularly if there's one that is going to declare war on you
7) You need to trade technologies, but be very careful about giving the major AI's a lot of money or good techs.
8) I personally play with "Tech Brokering" turned off. Otherwise it's just too much micromanaging with the technology.
9) Turn off "Auto Upgrade" of your planets. . . the AI is retarded and will totally mismanage your planet.
10) Build a ton of constructors (make a short range one that's cheap) to build economy starbases around your planets once the colonization phase is finished, and to build shipyards on your frontiers.