Most basic rule: don't automatically plop on your starting location. Look at the map, see if you can infer _IF_ there might be a slightly better location nearby. If you have worker, settler, or scout, maybe use them to expand your visible area a bit. Don't even be afraid to use your settler to scout out a bit.

Example: recent game I started as Gilgamesh in the HiTM mod, starts with Agriculture which reveals Wheat and Rice. I roamed around with my settler and warrior for about 10 turns looking for some wheat or rice but couldn't find any so I trashed it. Second time, I got the end of a peninsula, with a lake. Not the greatest position, but there was rice, so PLOP.

The one Prince win I've got on HiTM so far with Vikings, I had a decent spot in my initial start, but no resources (they start with hunting). There was a hint of forest down to the southeast. My warrior moved that way, and sure enough popped a map. There was an elephant and a deer quite a ways down southeast on a river. Still no sign of coastline, but I could tell that by moving toward those huntable areas, I'd get closer to the coastline. My initial city must have been 8 or 10 tiles from my initial start location (this was a huge map). The consequence of this was that my capital was only about 7 tiles from the Japanese capital. The consequence of this was that it put me into a position to steamroll the Japanese early in the game, and this was key to me winning.

Lots of other rules, but that one sort of gets it going.

ADDIT: The key in this, is creating a maximum workforce, ie. Workers.

1. Never place a city in that little blue circle. The computer is a cheat, and is trying to tempt you into doing something stupid just so it can win. It is evil and bad and wants you to lose.

2. Do not found a city in the sea. It did nothing for Atlantis, and Venice is regretting it too. Rising damp is a terrible problem, and you can't just pop down the road to the local pub for a quick drink when you feel like it; you have to swim, and there might be jellyfish.

3. Avoid mountains as they are full of yaks and llamas, and give deserts a miss too as they are crawling with snakes. So are jungles, come to think of it... And you get bears and wolves in forests so they're a bit dodgy. Avoid water (mosquitoes), grasslands (herds of fierce wildebeaste), plains (termites) and beavers.

4. Do not build on ice. Come the summer you might regret it when you discover you have actually built your precious capital on a lake. It is also good to steer clear of swamps, volcanoes, geysers, quicksand, floodplains, boiling mudpools and Aztecs.

5. I was going to say French, but thought better of it.

6. Have you considered remaining a hunter-gatherer society?

Really annoys me that desert is useless and mountains too . . . *grumble, grumble*

Aw c'mon Scip, there's got to be some useless stuff just for variety if nothing else. However, I do think that desert ought to be irrigated and made useful with, say, environmentalism, and maybe mountains made slightly economically productive with (?) combustion and corporation (tourism, skiing and the like)

For me, two or more resources is a must.  I usually don't worry too much about proximity to my capital as my 'superior' culture will usually fill in the gaps rather quickly.  If a rival does plant one of his cities in between mine it will most likely be flipped by culture anyway.  The main exception to the 'two or more' rule would be a choke-point to a rival's expansion, which I will race to  (and fortify) as quickly as possible, even if it means having to lower my science rate due to high maintenance costs.