Here goes nothing...
1. Start building a worker.
2. As soon as your population goes to 2, switch to settler. Once you`ve built your settler, switch back to the worker.
3. Depending on your terrain, choose your tech path.
If you have some plains with a river nearby and some forest in your territory, you can go for mining and then bronze working. The reason to go for this path is that you will be able to cut the forests, farm the plains and start producing Spearmen in your 2nd city very early.
If you have lots of unforested grasslands then go for animal husbandry and trapping. Your worker will simply build trading posts whereever possible. And if you`re lucky, a few camps too. The downside of this is that your 2nd city will have to build a warrior instead of the spearman. The upside is that you will have more gold per turn and the warrior takes less time to build. Important if your neighbour DoWs you early.
If you have 2 calendar resources in your city borders and 1 just outside (culture expansion will make it available in time) then go for pottery, calendar. As soon as you get your worker built, improve those tiles and possibly sell all of those resources off to the AI. It`s not probable but in case you do go into negative happiness early on the 30 GPT from selling your luxuries to the AI totally makes it up. And you should have enough money to befriend a city state and get your happiness resources from them.
4. Keep in mind that you should not spend all of your income away asap. If the AI attacks you early you should be ready to buy a spearman or atleast a warrior for extra defense.
This is appropriate for Deity difficulty. If you try this on Emperor then you are taking unnecessary precautions and possibly crippling your early economy. Additionally, i have only used these strategies in Marathon games.