For one you're not using tactical structures apparently.
You should also make sure you're fighting easy level computers if you just bought it. In time the computer becomes unbelievabley predictable. You should recall your fleet, but have another fleet ready to start the offensive if they invade, then have your moving fleet come back to reinforce.
Another thing, use pirates! Pirates are your friends. And scouts are your enemies, it lets other factions know where and what you have. If it's an advent scout, avoid the planet you destroy them at or destroy them at an unimportant planet. They have a feature that lets them look at the planet they were killed at for a while that's able to be researched. If it's a TEC scout, kill them immediately. TEC has a similar technology, it lets them deploy sensors while the scouts are still alive that are just like if you killed an advent scout, only the sensor can be sent out again.
As for attacking and defending, this game is very tactical.
Use long range frigates against short range frigates and heavy combat cruisers.
Use strike craft against long range frigates and heavy combat cruisers.
Use antistrike craft frigates against strike craft. (this seems like a simple concept, but it went right over my head in the last game)
Use repair/sheild cruisers a good amount of time and kill them first if the enemy has any.
Kill capital ships last.
Antistrike craft frigates and planet bombing frigates are only good at their specialty, never use them otherwise unless they can't do their job.
Know your capital ships and deploy them in the right situations.
Use fighters against strike craft and most frigates.
Use bombers against structures, most cruisers, and capital ships.

These are only some of the tactics in the game that you need to know to be victorious, but they don't apply too much to easy or normal computers, so don't worry too much, you'll get it.

Um... if deployed correctly, tactical structures can make quite a difference. True, if the attacking force is large enough, the best they can do is slow down the assault, but that should give you enough time to get reinforcements in.
Example Vasari tactical structure layout (usually works well for me):
Set 6 missle launchers in a circle around the planet's gravity well (these defend well against single targets, like Capital ships)
Build 4 Hangar defenses (good against most frigates, and you can use the missle launchers above to take out any anti-strikecraft ships. I usually have 4 fighters and 4 bombers)
Place a Nano Weapons Jammer so that the area it can hit covers as much of the gravity well as possible (On larger worlds, I set it close to the planet, and try to cover the area where I think my opponent will strike from)
You need to decide for yourself whether to place a Phase Jump Inhibitor or not. If the enemy gets "scared" when your fleet arrives, it will take 7x as long for them to jump away, which should allow you plenty of time to turn most of their ships into scrap metal. However, it is sometimes better to build a restoring structure, to keep your structures intact.
If properly built, I've seen this defense hold off pirate fleets of at least 4 tickmarks (on the side of the planet, that little grey indicator. I'm not sure what they're actually called.).

Good luck.
ChaoticMagician

another note on tactical structures against computers.

last night as i was playing TEC i witnessed the computer actually do something well. they waiting until my force was attacking a well defended ai with a decent fleet. then two other ai's attacked my planet with a fleet that had maybe 4 or 5 caps and 50 other ship types.

my planet had 6 hangers, a repair bay and the rest of the slots were guns. i had been building that planet as a forward ship yard as well. so it had 4 frigate yards, 1 cap yard, and all the other normal stuff.

so the teamed up ai's had the perfect setup. except they were slowed by my defenses. in fact there were slowed enough to allow me to finish off the planet i was attacking, then turn around and defend my planet with the loss of a single gun. also note that i was pumping out heavy crusiers from the yards, but they took a few minutes to finish. the guns and hangers gave me the time i needed to win.

between the 3 ai's that were involved, they lost 4 cap ships before withdrawing. So use tactical defenses against the ai. it will make a huge difference.