You are learning the hard way, but you ARE learning!

Also, that map have so many ugly features (tundra, ice, barren...) You have to make sure your second city occupies a great location, because your starting city sure does not.

You can build a new city with the Tribe unit, which unlocks at Tribalism (which is still a far way off in the tech tree).
Some other thoughts on the tech tree:
Shelter Building, Piercing and Cultural identity are all great techs that will help you a lot, I think.
Shelter Building unlocks a huge list of buildings, some of which gives you

and

.
Piercing lets you build Spiked Clubman, which have a base Strength of 3 and +25% vs. Melee. You need these guys to battle the Neanderthals (and please learn how to pronounce that!). They will soon be

on your door, and the CAN enter your cultural borders!
Cultural identity unlocks a building that gives the city +1
and +25%

. This will boost research by 3-4

per turn in total. Also, this tech lets you run Matriarchy, which lets you grow your city faster.