As a person who has never played a Civ game before what would be some general pointers to look for? From the few games I've played so far I tend to focus on getting religion and city states on my side so I've been playing Greece and focusing on patronage and Piety. Is this good?
If you're new to Civ, religion is probably something you shouldn't worry too much about. Science and production are what propels you towards victory.
Just some very basic pointers...
If you settle your first city in an area with plenty of green grassland, focus on growing the population of your city and push for science as hard as you can. Do this by choosing the social policies under Tradition and getting a library built ASAP (tech needed for a library: writing). After which, you should research towards Philosophy, then Civil Service and then onto Education.
Upon discovering Philosophy, build the National College in your capital for a 50% science boost.
Upon discovering Education, build a University for another boost to research.
Once you've got your universities up and running it's time to make a decision; should you continue along the path of science, or should you switch to war and begin researching the lower path of the tech tree? The choice is yours.
If you settle your first city in an area with plenty of hammers/production, focus on expanding wide (having numerous cities). Do this by choosing the Liberty social policies. With Liberty, early wars are quite beneficial, so instead of pushing ahead with science, focus on researching techs that will help you war. research towards archers, horses and catapults, then go and steal some cities from your neighbour. Try to get three cities of your own first, then build 2-3 units in each before going to war.
Once you've stolen a few cities, you can then make another decision; should you try to steamroll the rest of the planet, or switch over to a more peaceful style of play? The choice is yours.
However, with mass expansion comes unhappiness. Before you begin an onslaught, try to gauge how much unhappiness it might bring. You can counteract unhappiness through various social polices and religion beliefs.
Other pointers:
If you have more than 1 luxury, you should be able to rent it to another civ for 6 gold per turn (or 5 if they don't like you). Every few turns, go and talk to the other leaders and see if there's anything you can rent to them).
Want to weaken an opponent before attacking them? Bribe then into war with another civ. You can do this on the lead screen where you strike deals, look on the left hand side and one of the options should be 'Declare war on'. Usually you can start a war for as little as 100-200 gold. A bargain.
City states are your friends, never attack them. Try to ally with one's that suit you and
-are 'Friendly'
-have iron/horse/coal resources that you need
-have happiness resources that aren't within your own borders
-are located at natural choke points.
Finally, the game can be a little overwhelming, especially as there have been two expansions since launch. If you're finding everything a little bewildering, I suggest that the next time you play, go to the DLC menu from the title screen and uncheck the Gods & Kings and Brave New World, so that you can experience the base game without religion, trade routes, tourism etc