The boom or eco/tech rush focuses on using all of your early resources to quickly get a strong economy up and running and to quickly proceed through the tech tree, while mostly - or even completely - forgoing military research and training military units.
Be sure to quickly seize and maintain control of areas that contain resources, especially with rare resources. If you cannot do this, it is possible to focus your attention elsewhere and you can construct a military force to conquer that area or forge an alliance. Allied nations should permit your merchants to collect desired resources that they have within their territory
When booming, you're either aiming for a peaceful victory (wonders, tech race to end age) or planning to wage wars sometime later in the game when you can steamroll your enemies with more modern troops while they're still stuck in the past.
You will need to focus on researching Science, Civic, Commerce tech and age advances (in that order) to get your economy up while researching Military tech only to increase the pop cap as needed. Aim to build at least 4 cities, each with a University full of scholars. Most of the Library research from level 2 on requires knowledge and quite often you're lacking this one (especially when playing with slow+expensive tech like I do). Each university generates 45 knowledge early on. If you're lacking the space to build more cities, build the Hanging Gardens for another 50 knowledge.
Recommended library research:
- Research Science 1 for cheaper future research and temples (gives access to taxation for early gold).
- Civic 1 to build a second city.
- Commerce 1 to increase the commerce cap from 70 to 100 and to build markets and/or docks.
- Civic 2 to build a third city (might postpone this if you're Bantu or planning to build the Pyramids).
- Classical Age (if you're playing with slow+expensive research, you might want to advance to classical before researching Civic 2 to get up universities and knowledge production faster). Build universities in all cities and start training scholars.
- Science 2 for cheaper future research.
- Military 1 to increase pop cap (for more workers and scholars)
- .... (as needed)
When tech rushing, you're somewhat prone to early rushes and large enemy armies.
If you're Maya, simply rely on the extra atatcks from cities to deal with early rushes. If your playing a different nation, garrison 1-2 archers in each city and build towers and garrison them as well.
To counter army attacks and siege engines, create a small cavalry army consisting of a patriot and several light or ranged cavalry units. When an army shows up, try to flank it, ignoring all infantry and cavalry, while heading straight for their support: Kill patriots/generals first, next the supply wagons and finally the siege engines. Then retreat your surviving units and let the attrition finish the job.
The Colossus is probably the best to get early on for it's 50 population (requires less military research), extra gold and timber/gold cap increase. Pyramids are ok as well for it's extra city and food. Hanging Gardens are only useful when playing with slow + expensive tech. Get the Terra Cotta Army to receive free units you can use to defend, so you don't have to produce them yourself. If you have many rare resources or are in an alliance/team, build the Porcelain Tower to increase income from these.
If you're going for a peaceful victory, Consensus Government types (the green ones) are usually the better choice. If you're planning to go to war later, you might want to adopt Totalitarian Government types (the red ones) to reduce military prodction cost and time.