Here are some things I've found to be good for me in my games. Adopt them or bash them with a hammer... it's up to you.
~Exploration - this is a lot more important than it used to be because now trade routes are tied to what cities you know exist. Having two scouts and a naval scouting unit out as soon possible will help you be able to maximize the value of your trade routes early on.
~Trade Routes - like I said above, really important now. Get them up as early as possible, particularly naval trade routes as they provide even more gold. That being said, make sure you're able to protect the integrity of your trade routes. War and barbarian incursions can disrupt your trade routes and absolutely wreak havoc on your economy. Once you've got the World Congress going, don't underestimate the value of having diplomats in the cities of civilizations that are of strategic importance. The ability to trade votes cannot be understated. Early on, it's likely that someone you're trading with will be embargoed, and I've also noticed that other civilizations like to put up the "Embargo Trade with City-States" proposal. You'll need to be able to protect your economy diplomatically, so make sure you've got a few diplomats hanging out.
~Happiness problems - I'm not sure what your playstyle is, but hold on to at least one copy of every luxury resource you have. If happiness is a problem for you, you might want to think about trading luxury resources for luxury resources you don't have. Also, City-States are a good source for this as well. Befriend them, buy their allegiance and you'll gain access to their luxury goods. Also, make sure you're leveraging the social policies to their fullest extent. If happiness is still a problem for you, try playing as Portugal for a while until you feel you understand the rest of the game's systems well-enough to tackle the happiness problem head-on.
It's worth asking what game stage he's reached, since he may be suffering adverse effects from ideology.
I've had a good run with happiness in my current game, but it has occasionally been an issue - being Indonesia with two off-continent cities helps (this can also help a lot with gold issues if you make Declarations of Friendship, or if you trade your luxuries for gold per turn. Unlike every other civ in the game, Indonesia can rely on having luxuries that no other civ will ever possess, so it can always trade resources with somebody), but having Samarkand as my closest CS was certainly required to balance the happy books from time to time.
Some religious tenets are very good for happiness, but bear in mind that a common G&K choice - Ceremonial Burial - has been toned down (it's now +1 happiness per 2 cities, not per city), so if you're used to relying on that you may find you have difficulties. Also, most happiness buildings produce less happiness than they used to. Another thing to watch for is horses and ivory - circuses haven't changed, and are therefore now excellent. I lucked out here as well: I have four of five circuses in a 7-city civ.
Trade routes are very important, especially early, but they aren't your only source of gold. If you can get it (and it's still not an AI priority - on Prince you should have no trouble), the Mausoleum of Helicarnassus is arguably now one of the most powerful Wonders in the game, as gold is rarer and Great People more common. A couple of times this game I've found myself doing something I never did unless I ran out of buildings to construct in the past: set cities to Wealth production.
The religious belief Tithe is better than ever - in my current game, by the 19th Century it's earning me over 60 gold a turn. Piety now makes faith somewhat quicker to generate, and religion is if anything more important than in G&K.
Also, if you're used to building lots of buildings and units, try to look through what you've built and scrap what you don't need - with gold generally in shorter supply for much of the game (I have a large income in my current game, but trade routes are not the biggest contributor), you will need to specialise more. This is particularly the case because you will now mostly need. You may well be able to get by with fewer units - I've built very few (but then I am using Convert the Heathen as a Reformation belief, which is very possibly completely overpowered). My two games so far have been mostly very peaceful.
Consider having one or two "trade hubs". The best cities for this will usually be on the coast, and with either a lot of strategy and/or luxury resources, or by a river (the best sites have both, but usually if you have at least two resources, at least in the early game using caravans this will provide a bigger benefit than rivers alone). This way you can build fewer caravansaries (but not harbours - any city you can't connect to your road MUST have a harbour, since the gold you get from overseas "city connections" is, at least in my experience, the single biggest non-religious, non-Wondrous income earner. Plus harbours boost trade as well). Bear in mind that trade routes have limited range, so the trade hubs should be accessible for the major civs/city-states you want to trade with (these will ideally be ones that don't share the same resources as your trade city).
Finally, for subsequent playthroughs try civs that have benefits to gold and/or happiness, or (like Indonesia) abilities that you can use to generate these, so that you can get a hang of the new game without worrying so much about happiness and gold.
Probably wearing them now. 
