Top Ten Tips to Remember
1. Aim for technologies which allow you to hook up the resources around you. No use researching fishing if you are not near any fish!
Good point, but one critical thing I haven't seen mentioned here yet (apologies if it has) is, when making decisions about research, weigh shorter and longer term interests. In other words, don't always just look at the list of techs you can
immediately research (the ones that appear in the popup window after you complete a tech) but go into the tech tree and also see what role each of these choices serve as gateways to later discoveries.
For example, it may be that there is no need for fishing, but it will open sailing up, and you may want to get trade established on coastal tiles to boost commerce & keep subsequent research from being bogged down by expenses. Not the best example, but there are many many case of techs that may not may not be directly critical, but are the keys to discoveries that are. A good example is Mysticism, unless you want Stonehenge or Monuments it does nothing -- and you probably care little about those if you are a creative leader, for example -- but you really, really want the techs coming right after it, ASAP if you aim to found early (and dominant) religions, build the most important early wonders such as Pyramids and Oracle, improve city happiness or defenses. and/or hook up resources such as stone or marble. So maybe you research mysticism even if something else is more immediately beneficial -- say, fishing, if you
do have fish that you want to hook up.
It's that complexity of decisions, the need to weigh short and long term goals in decisions, that makes Civ the incredibly deep game that is. The "right answer" of what to do next is entirely predicated on how you phrase your question!