Is it something that's done automatically? Is there a way I can maximize their effectiveness by managing them?
There's lots of ways to maximize the effectiveness of trade routes. In fact it's possible to power your economy by almost trade routes alone.
First coastal cities. Only coastal cities can build the two improvements that improve trade route yields, Harbors and Custom Houses. Plus only coastal cities benefit from one of the cornerstones of pursuing a trade route strategy, the Great Lighthouse.
Explore! Get a galley out sooner rather than later. Follow the coast and make contact with distant civilizations. Sign open borders and start bringing in that trade income from distant routes.
Avoid War. Not only do you get a bonus on your trade routes for "sustained peace", trade routes that pass through your enemies territory will be cut off for the duration of the war robbing you of income.
Sailing techs. The sailing line of techs is all about trade routes. Most of them allow you to more effectively explore for trading partners, increase the yield from trade routes (compass), or even give you more resources to trade around with all these civilizations you're meeting (calendar).
Astronomy deserves some special mention. Oversea trade routes are huge, giving huge bonuses to the yield of the trade route, easily bringing in 8-10 commerce a turn (on coastal cities). That's better than a fully developed cottage, even with printing press and free speech - and consider that each city can have from four to five of them which require no citizens to work. That's massive. If you have some overseas trading partners and a decent number of coastal cities, astronomy can easily increase your research 50 - 100% on the turn its discovered.
One pitfall here. Enemy AIs love mercantilism which will sever their trade routes with you. If mercantilism becomes widespread you have some options.
A. Switch to mercantilism yourself, and go for Statue of Liberty w/ Representation. (If you can't get the foreign trade routes might as well get the free specialist instead)
B. Use espionage or diplomacy to switch their economics back to decentralized or free market.
C. Tech up to communism and trade it around. AIs tend not to like Free Market enough to switch to it once they get Economics, but they'll happily switch to State Property once they get Communism and this will open trade routes back up.
To sum up consider trade routes as an economic strategy if some of the following are true:
- You can secure a lot of coastal real estate - REQUIRED
- Can build the Great Lighthouse
- Suspect that there is an AI or two lurking overseas
- Have some resources calendar can open up
- If you are playing a civ that has a sea-based UU or UB (Vikings, Portuguese, Carthaginians, ect.)
There ya go, that's most of what I know. Feel free to ask more questions, tho.