Out of settler?
I play on Prince so what some of what I'm saying won't apply going higher than that, but these tips should help you move out of settler:
- Make sure you build a Scout either 1st or 2nd in your capital - they can replace your Warrior running around the map and find ruins. You can put them on auto explore, so you don't have to micro manage their movement.
- With your early culture, I recommend taking Liberty - that way you can pick perks that get you free workers and even a free settler for your 2nd city. (Note: you can also have your workers on auto, which works just fine on Prince)
- For early tech, try to look around at what resources you have in your area. (Don't need to get mining if you don't have stones nearby, for example).
- Set your cities to optimise for food. Again this doesn't exactly transfer over to difficulties higher than Prince, but it cuts down on micromanaging so you can get comfortable with empire building, and food focus works absolutely fine on Prince. You want food focus (and to limit the tiles you buy, unless it contains a luxury resource), because no matter how big your borders are, those tiles won't get worked unless your city has a high enough population - having more food leads to higher population and thereby helps your production and science as well, because you're working more of your city tiles.
- Avoid building wonders early, they normally aren't worth the no. of turns spent on them until your production is higher. AI doesn't often beat you to wonders on Prince anyway, so you can afford to wait.
- In support of food production, use caravans to send food between cities, especially to new ones so they get online quickly. Focus on building things like a Granary, Water Mill etc to support food production. Settling near lakes or on the sea (and building Lighthouse) can also help.
- You don't need much military if you plan on playing defensively, you can check your rank on the Demographics menu and see how much force you have compared to the AIs. Getting spearman relatively early can help you clear out bandit camps and I always find archers useful but honestly I play less aggressively than many players and try to build out my food and gold growth rather than army in the early game.
- To support growth, make sure you build a shrine and use your Pantheon to support faster growth rate, this can be especially improved once you make a Religion by the "swords into plowshares" belief, as long as you aren't planning on playing super aggressive.
- Remember your cities can't make food while you're building a settler - that's why I think Liberty is good for your first settler. Nonetheless, it's normally good to get to 3 or 4 cities as soon as possible - as long as you manage your food growth well you should be fine.
- Build more workers than you think you'll need. I wasn't building enough before and I underestimated how much that was costing me in getting new cities to a useful level of production.
- Get catapults early-ish, make sure you have a siege weapon placed on all your cities if possible, as it makes them much harder to take early game.
- Once your early food buildings (esp. Granary, camps etc) are teched up, try and get to unlocking Colosseums, unhappiness is really bad as it sucks out all your population growth, and the Colosseum (on the bottom tech track, after spearman), is really useful at keeping that off.
- If you're going to play aggressive, better to take on city states with a few catapults early rather than waiting till later. If your population and science hasn't been doing well you just won't be able to build enough quality units to catch up by conquering stuff mid-late game, the city defences just get progressively stronger.
Hope these help, just some of the ways I think my play has changed over the past 90 hrs or so since I moved up to Prince on the regular!