haven't figured out how to allow trade with specific empires/etc..
You can only do a generic "I let people trade". Go to "Manage" on one of your planets, then tick the "Allow Others to Trade Here" box and then set a tariff. People can then send trade ships to that planet. If you want to trade with someone, look around for a planet that allows trading and send a trade fleet there. From there, I think it's automatic - trade ship goes to their planet, then onwards to another trading planet, then eventually back to your planet with the profits.