Method 1:
You need lots of gold for high science, so right from the very start you should set wages as low as possible and also build gold enhancing improvements like bazaar, bank, broker etc. My first wonder is always pyramids since it gives gold bonus forever. On impossible this gets me to diamond age by mid 1900's.
Method 2:
Get friendly with a high science civ (check out the rankings graph to find which one) and forge a science pact. For a bit you have to buy the advances off them but after a while they give them to you. This especially works well on impossible since AI gets ridiculous science bonuses (like, they discover an advance once every 2 or 3 turns without even having a big economy) and so you can reap the benefits. I've got to the diamond age by this method in about 1750. Once the civ's usefulness expires you can wipe them out.
Hope this helps