First of all it depends if you start with a civ, that has an unique unit/unique improvement in the early eras. If you have them, you are already better off, as they give easy era score. Other than that, here is a short guide on what to do:
I like to start the game with a scout. It lets me find other civs (+1 era score), tribal villages (+1 era score) and world wonders, which also give era score. Then I like to have a couple warriors dedicated to hunting down barbarian encampments, as they give a fairly big amount of era score (2 or 3 depending of if the camp has been activated or not). These are usually good enough to get you to a normal age.
Getting a golden age is a bit harder, at least on harder difficulties, as the eras change so fast. For that some useful things are as follows, settling on a world wonder gives you era score, having your first naval unit gives era score and finally becoming suzerain of city states gives you easy score. This can be easily done by sending the governor Amani to city states, as she gives +2 envoys to the city state she is in. If you have city states with 1 envoy, just send her there and you get easy erascore.
Finally, if you are doing early warmongering, you can get a lot of era score by capturing enemy capital and their last city. This can help you on a domination focused game.