(I know this probably isn't the thread for it but)
Here are some really basic pointers which should get you playing quickly, rather than better.
Play on a low difficulty.
When you start the AI will have dumped your settler in a place which is perfectly fine, until you know what you're doing just settle there.
You can send your initial warrior out to explore, you can attack barbarians, but I wouldn't attack anything else until later.
Units you can build:
Scout- good for scouting, don't want more than 1 though.
Builder- used to improve tiles (some you'll need a tech for). Builds farms and mines mainly. Can only improve 3 tiles before they're gone.
Slinger- weak unit, can be upgraded into an archer later, but not very useful
Warrior- first basic combat unit, build a couple of these to protect against barbarians
Settler- gets you another city, but you lose 1 population when built. Build one of these after a couple of the above and perhaps a monument.
Buildings you can build:
Monument- useful for getting early culture
Granary- not needed initally really, but as you get more people it's useful.
When you settle a city the AI will choose where people work. Each tile grants something (unless its flat desert or snow)- either food (grows you pop), industry (builds things), culture and science (go down those trees), faith (used to buy religious units (and others down the line)), gold (used to buy everything). These are also granted by buildings and wonders. Some tiles are luxury resources- when improved by a builder they will provide amenities to keep your people happy. Some are bonus resources, which just improve the yields on that tile (such as extra food). Some are stragic resources, when you improve these with a builder each turn you get 3 of that resource (such as coal). Some units need stragic resources to be built. Generally, just ignore choosing tiles, the AI can do that, and use builders to improve tiles with things on them.
Districts. This is the main change from other Civ games. As you advance down the tech tree you'll unlock districts. These can only be built if you've a high enough population (something like 1 district per 2 pop). Each district has a speciality- campuses for science, encampments for land combat etc. Some of them have 'adjacency bonuses'- if you build them next to something (like campuses next to mountains) you get a bonus. This is shown clearly on the map screen, and you want this number to be as high as possible. After you've built a district it will have unique buildings you can build in it.
Science and culture have respective trees. Science is all good- better buildings, improvements, powers etc. Culture is also all good, but unlocks governments and policies. Governments give you inherent bonuses, but more importantly more space for policy cards. Policy cards are in 4 flavours- military, economic, diplomatic and wild. Each one can only go in it's spot (anything can go in wild). If in doubt for culture choices just scroll to political philosophy and select that, and after that exploration. The AI will then beeline to those and give you powerful governments.
Combat is as simple as marching your troops into the computers. If you are weak they will declare war on you. Walls are a must for defending, they can't be bought and have to be built. Generally the superior teched units will win. If you see a scout with an exclamation mark at your city the barbarians have found you. Get some troops to follow it back to its base and kill it.
Great people- throughout the game you will recruit great people by accumulating great people points. Generals and admirals just need to be near troops for their bonus to work, artists and writers need buildings in theatre squares to produce works, everyone else just use them in their district.
Housing- the more people in a city the more houses they need. If housing is full it takes loads more food to grow your population. If you settle next to fresh water you get more housing.
Diplomacy- with the base game I think it's just a matter of trading with each civ as and when. Just try selling them stuff.
Religion- don't worry about this.
Wonders- take up an entire hex, the AI will often beat you to them, but on lower difficulties you can get them if you want them. I'd play without them at first until you've got to grips with the game.
I think that's it. At the start of the game you can't travel on water, and mountains will also block your travel.
Edit- City States! There are some solitary cities with no leaders. They can’t settle any other cities, and just mind their own business. Roughly every 100 turns you’ll get envoys to send to these states. This will get you bonuses, and if you have more envoys than any other civ, and at least 3, you become the suzerain. This means you get a special bonus, access to their strategic resources, and can pay to borrow their troops for 30 turns.