Can't win on chieftain

Apparently I'm a total fail at Civ. I played on "Settler" difficulty and won a game pretty easily, but when I started playing on "Chieftain" (which is only the next one up) I did REALLY BAD point-wise. I had like five other civs and was last or second to last in points for the entire game, amd I was like, WHY??? I was the most advanced civilization, thouhh I only had a few cities, and I lost a war early on, but really. Then I played another game on a big map, and I'm doing better, there are 9 civs and I'm like fourth or fifth worst. I'm at around 1850 and researching Steam Power, just made peace with Charlemagne (he demanded tribute, but I refused and beat his obsolete army of Knights and Pikemen with my unique French units), I'm not really good at war but I only have four cities and zero room to expand, so I'm thinking about taking one of his cities. Any thoughts??

Post a game in Strategy & Tips forum. Post screenshots too, and play only small turnsets, wait for the people to give advice there. There is someone starting on Chieftain level atm., maybe you wanna play that game with him. You lack understanding of base-mechanics like improving tiles, improving them right, working them, expanding to as many cities as possible, building an army and so on. You'll get all that advice in S&T if you're patiently.

P.S.: Points don't matter at all, they're mostly made by population, techs and world-wonders almost don't matter. Also, bigger cities are not necessarily better.

ok thanks I'll try there