Start building lots of cities and make them science. Put Libraries and Universities in all of them. That way you can get more science and more science=advance through the era's faster. --- In Soviet Russia, ROFLCOPTER laughs at you!
don't forget about backfilling too. you can expand, make buildings or troops, or whatever else you need to do. when you switch to tech you will backfill any techs that you can do in 1 turn, as long as they have been done. its very common for me to tech slow (or collect gold) while i build some libraries and settlers. then i switch to all tech, pop democracy, and blow into the lead.