there is a collection of tips over at the strategy subforum although they can be somewhat obsolete depending on the build you're playing
-get a second city asap: either but founding it yourself, taking it from the greys or using tricks like the liberate outpost
-don't overbuild quarters, don't neglect infrastructure
-explore, hunt and ransack
-attach 1 territory to your initial cities, build EQs and potteries to get enough INF to keep expanding. choose civics woth the same objective
-claim lands with natural wonders and powerful luxuries such as silk, dyes, marble, papyrus, lead
-build wonders and holy sites once you can get them done in 3-4 turns at most combining your cities or when your closing in on revolts
I might try following some of this advice myself, but it seems a little high level for just learning the game.
I personally found that a attaching two territories to the first city was an easier start to learn from, since you get more food and production and have an easier time creating districts and units. Also if you capture grey cities you will quickly fill your city cap without founding any of your own.
Build as many makers quarters as your stability allows, while keeping your food positive. Most EQ are worth building early but be aware that building a few makers quarters before a non-production EQ is often better. Luxuries (built and bought), religious sites and canals are good sources of stability’s but I usually wait until production is high and stability is low to buy them.
Build up 4-8 units and allow greys to found cities, and focus your aggression on them. As you develop, I recommend focusing on conquering an AI, but it may take a few eras to get the pieces together at the right time. They also may just declare on you. The key is to win the war in defense or in battles in the field. A mix of archer and melee holed up behind cliffs can even the odds very quickly, and my early games were largely about forcing a superior force to surrender by winning these defensive battles. Especially as the AI gets advanced units pretty quickly, this can help win wars and earn a few territories and gold at the era transitions.
Conquering cities is a bit tricky at first while they still have a standing army. AFAIK siege weapons don’t really work right now, since AI will sortie as soon as you attack the city, preventing you from building them. So just fight the armies in the field.
When you do start to fall behind on tech (eg struggling to get to EU unlocking techs) begin investing heavily in science. You can take a science culture and/or build a ton of research quarters. The key is to build a bunch of them in one place, since they give each other a strong adjacency bonus. Also don’t neglect to slot pops as researchers. The +6 science each is actually quite a bit and enough to get through ancient and early classical techs reasonably quickly.