Pirates are really easy to figure out-

I turned them off till I read about them - basically when you hear 'pirates are forming a raid' click on your black market button, then the pirate tab.

On the left it will show the pirate target, usually you, now here is where they can be a good thing - click the bounty increase button beside an enemy of your choice. As long as you bid more than anyone else you will make them the pirates target.

You can see if you are ahead in the bidding as on the left the target of the pirates will change to the picture of the person with the highest bounty on their head.

Since I learned this I haven't had a pirate invasion and have used them to help me soften up nearby foes and anyone that I just generally didn't like.

Hope this helps.

As was mentioned, you can turn off the pirate raids by using the "game options" button that appears when setting up the game.

If you choose to leave them on, you have two defenses:
1. Outbid other players so the Pirates attack them
2. Kill them when they show up.

I know 2 isn't as easy as it sounds, being a newbie myself. The best way to do it is to make sure you get your free capital ship (the first capital ship you build costs nothing except the cost of the factory and supply). Which capital ship you make is up to you, personally for dealing with Pirates I favor the direct heavy hitters (like the Kol), while I find that the Carrier types just aren't strong enough at level 1 to deal with a Pirate raid (maybe if you can afford to train a Carrier to level 3 it'd be more worth it, extra fighters would help).

Research the Repair Bay technology.

Early on you'll want to use your ships to go out and take a couple of planets. When "Pirate Raiders are on the loose!" gets announced, you can use the Pirates button at the top (looks like a skull I think) to see who they're attacking. The person with a sword icon is the one the Pirates will come after.

If its you, send your fleet back to your home world (thats where they seem to attack most of the time for me). Build a repair platform or two (two with some overlap in their area of effect is very effective), and park your fleet inside the radius of the platforms. When the Pirates show up, the repair platforms give your ships a major advantage in fighting them. If you can kill them off, your capital ship will gain a lot of experience and probably a level. You'll probably have to do it two or three times, but each time you should be growing your fleet and trying to take more planets in between Pirate raids.

Another trick is that if you know where the Pirate base is (its a planet that has tons of Pirate ships around it, don't attack it without a big force!), you can snipe the Pirates off. For some reason I find that they often don't engage ships on the way to their target, they just keep going. So if you know they're coming after you, your fleet can meet them a planet or two away from your home world, take some shots at them, then follow them to your home world. That way you soften them up a bit before the fight really starts.

After a night of experimenting while dying to them constantly, I found that these tricks work for me (on Easy and Normal difficulties). Good luck.

Agreed with the other posters. A few turrets and one (I prefer two) hangar bays is enough to hold pirates at bay while one of your fleets sets course to the attacked world.

Also, remember, attack the PILLAGERs first. They are the bombers. Once they are gone the only real harm the pirates can do is to objects in orbit. Your planet is safe.

A good player or AI, however, will use a pirate attack to their advantage and sometimes coordinate their attack with the pirates. Gotta watch out for that too.