Probably the biggest thing a lot of new players don't notice is that when you colonize a planet, it actually drains money from your income and you need to upgrade its Infrastructure (first upgrade option) before it starts generating money through population taxes. A good rule of thumb that works for me is that you should expand when you can afford this upgrade as soon as the planet is colonized.
Always go after the asteroid next to your homeworld first, it's cheap to upgrade to get rid of the credit drain, and if you get lucky and get 2 ore and 2 crystal mines, it will greatly speed up your resource income.
If you play TEC, which I highly recommend as you're starting out, you can get trade ports with only 2 civic labs and those are a great help making credits for you.
I would also advise to not rush research in the beginning, only research what's really important (Volcanic/Ice colonization if you have either of those near, trade ports, broadcast centers, ship hulls). Leave the weapon upgrades for a little later, in the beginning the number of ships matters a bit more than a slight damage increase.
This is all pretty general, but if you post with examples of what you're doing when you play, you can get better tailored suggestions