Some tips:
1) Try to grab a bunch of planets that have few connections to the rest of the universe (it depends on your map type whether this is feasible). This really cuts down on your defense requirements.
2) Try to research more turrets. These are really cheap defense (use a rebuilding drone to rebuild them for half price). Use gravity turrets to ensure that the AI ships have to spend a long time near those turrets.
3) Try to play much faster. You should be able to conquer the 5-6 planets well inside the first hour. The sooner you conquer the first planet, and go on to the second, the less time all other planets have to gather reinforcements, the easier it gets.
4) Because you build so many ships so rapidly, ships *seem* dispensable. They are not (until the midgame). At start every ship is precious (except fighters). Every ship you lose, sets back your timetable.
5) Use fighters a lot. Fighters are very durable for their cost. Make sure that in the early stages you use plenty of fighters (but not exclusively). Use combat strategies like: first attack with fighters, once these are engaged, use the rest. This helps with #3 and #4.
6) Regularly weed out damaged ships and repair them with an engineer. Cheaper and faster than rebuilding. This helps with #3 and #4.
7) Plan ahead. Once a planet is cleared, there should be a finished colony ship plus engineers waiting near the wormhole. This helps with #3
If you plug a wormhole with a forcefield (you build the forcefield over that wormhole), enemies can't enter that wormhole before they kill the forcefield. This is the only 100% (well...almost) defense you have.
9) Mass. Always attack with much more than the AI has. Never give him an even fight. Look again at item #4.
10) Against waves. Learn what works against what. If you are hit by a cruiser wave, keep all your fighters out of harms way and attack with all your bombers. Same for other waves.
11) Production. As soon as you can possibly afford it, research the first Economic Orbital Station and use it. These will put your production on steroids. Never research the mining improvements. As soon as you can possibly afford it, research the second Economic Orbital Station and use it.
This should get you going....