I alaways underexpand in my Custom Games, no matter what scenario it is or which size it is, and I end up waaaaay behind in tech by turn 120.
At what rate should I expand, guys? Should I build stupid filler cities on crappy terrain?
My early mistakes:
1) Making large empires with few cities. Now I worry about core cities for production, commerce, and GP. Then I fill in trying to make a bunch of 7-10 sized cities, that have some food sources, so I can whip the needed buildings for research, espionage and if applicable, commerce.
2) Use the power graph, the AI does. My game changed once I started using this, it's now invaluable. There's no need to build a defensive army twice the size of my neighbor, even if it's Monty.
3) Build stuff you need, nothing more. Does a +6 happy city need a colosseum? Probably not. (Unless you need the culture points).
4) Have a plan. I tend to settle city one, and start scouting for city 2, bee line for bronze working so I can start chopping out settlers. Cover needed techs, and then it varies. Usually shoot for Code of Laws for a religion so I can fund the empire, Civil Service for Bureaucracy, Education to start building/whipping Universities, Chemistry and the Liberalism to get free steel. Plans change, and it might be different, but have one from turn 1.
5) Whip whip whip. Make small cities with little but food productive. A bunch of small (7-10) cities with libraries/universities/observatories/monasteries goes a long way. Plus they may great guided missile pumps in the modern game.
6) Specialists. Ignored them in my early games. I've learned. People much better at this can probably go into it in better detail. If you a library, and resources to support the two scientists it allows, and you aren't, you're letting the AI win the tech race.