Feel free to disagree or add on, but after 6 partial games here's what I've painstakingly learned. 
1 - Watch your civics. This one has killed me. Just because you can change, it doesn't mean that you should. I've crippled 2 games by having high upkeep, which practically halted my research.
2 - Definitely don't always build what is recommended. I was just playing a game that had no free space, but I was being advised to build settlers!
3 - Watch you city growth if you don't want to start building health improvements. For my border cities I've manually stopped the food intake to stagnant to keep from needing to build costly improvements.
4 - This is one change from Civ3 that I'm not sure I like....if you are building a Wonder you can chop down trees and they add production to it. Personally I hope this changed.
5 - Pick on lesser civs at your own risk. No longer does a 3 city civ mean easy pickings. I haven't looked into the support model, but I got clocked by the Aztecs who I was doubling in victory points and had 15 less cities than I did. They were pouring units at me!
Have fun

1 - Watch your civics. This one has killed me. Just because you can change, it doesn't mean that you should. I've crippled 2 games by having high upkeep, which practically halted my research.
2 - Definitely don't always build what is recommended. I was just playing a game that had no free space, but I was being advised to build settlers!
3 - Watch you city growth if you don't want to start building health improvements. For my border cities I've manually stopped the food intake to stagnant to keep from needing to build costly improvements.
4 - This is one change from Civ3 that I'm not sure I like....if you are building a Wonder you can chop down trees and they add production to it. Personally I hope this changed.
5 - Pick on lesser civs at your own risk. No longer does a 3 city civ mean easy pickings. I haven't looked into the support model, but I got clocked by the Aztecs who I was doubling in victory points and had 15 less cities than I did. They were pouring units at me!
Have fun