The AI doesn't use it well.
Make sure you are aware of the enforced peacetime (and if you agree to extend it or not); IIRC it is only 10 turns. This determines if you should buy a lot of military units or not
If you have a guarantee of some peace (such as a very large map, or an agreement for early peace), buy a lot of techs early on, particularly if you can beeline for something interesting. Then buy enough cities to be able to keep up, and several workers. (Number of cities is affected by the time you advance to, of course.)
Always try to buy at least one expansion of culture per city; IIRC there are rules regarding where you can place a second city (and units, etc.) related to your cultural border. Take advantage of that. Culture is cheap, at least for the first expansion or two.
Don't buy very many improvements of your land, workers can do those quickly. Just buy 2 workers/city.