Hello. I'm new to Civilization series - started with V, <20 hours played. More familiar with Galactic Civilizations.
After getting hold of the controls on Warlord, I am starting to tackle Prince. I don't even play part first 50 turns because it's obvious I'm doing something wrong. Constantly out-teched, score in the lower half. There seems to be some problem with my tech order (I don't have one) and with my city-building choice, I tend to only search for spots that have at least one food resource and one other resource I don't yet have, those are almost always snatched from me if I don't go Liberty (and I don't often go Liberty, I have barbarian infestations to deal with), but even if I claim them, they lag behind (40 turns building monuments, etc) and also tend to be near the enemy borders, resulting in a DoW like two turns later.
What do?
After getting hold of the controls on Warlord, I am starting to tackle Prince. I don't even play part first 50 turns because it's obvious I'm doing something wrong. Constantly out-teched, score in the lower half. There seems to be some problem with my tech order (I don't have one) and with my city-building choice, I tend to only search for spots that have at least one food resource and one other resource I don't yet have, those are almost always snatched from me if I don't go Liberty (and I don't often go Liberty, I have barbarian infestations to deal with), but even if I claim them, they lag behind (40 turns building monuments, etc) and also tend to be near the enemy borders, resulting in a DoW like two turns later.
What do?

you don't care about that stuff too much and push your science through high pop (for OP, he doesn't really play for culture. He's bloodthirsty warmonger beast
). When I play for 'culture' I rarely build more than 2-3 libraries. In core cities only. I also don't annex much. Too cheesy for me. But here a newcomer tries to learn the basics and NC start is a solid strategy you cannot get wrong with.