Are you playing Twilight of the Arnor? Then my suggestion would be to start by playing the Terrans - they have the most standard tech tree, of which plenty of technologies are also used in other races' tech trees.
There are plenty of topics discussing the order in which to research techs over at the Galciv 2 forums, however I can give you some general pointers that work for most games:
1) At any given time, scroll through the cheapest (i.e. fastest to research) available techs and choose which one would bring the most benefit at that point in time
2) In the very beginning of the game, focus on cheap techs that give you percentage improvements in social production, military production, research, economy, morale or population growth.
3) Next it's often a good idea to research yellow techs from universal translator until trade so you can build an econ capital (great econ bonus, helps a lot to get your early economy back in the green)
4) Then on to (blue) advanced computing so you can build a tech capital.
5) Then some more orange production techs (forgot the exact name) so you can build a manufacturing capital, both for the production and for the econ bonus
6) If you're playing a galaxy of medium size or larger, now might be a good time to research down the light blue engine branch (nothing that takes you over 5-6 turns, but at least get to impulse driver or the next in line so your colony ships can grab those planets faster)
7) Keep an eye on the military rating of your foes. As soon as you see them go above zero, it's usually a good idea to research (red) space weapons, preferably also (pink) medium hulls and a basic weapons tech such as (red) laser / mass drivers / missiles. That will allow you to get some military up, which in turn will help to deter the AIs from attacking you.
8) After that the choice becomes much broader and depends heavily on what you need the most... Here I would recommend to revisit point 1) and see what's most vital for you to research, yet doesn't cost you ages. In my opinion for a traditional playing style it's often good to first advance a bit in production technology; once you have that it will be faster to transform any buildings into more advanced ones (e.g. transforming basic labs into more evolved ones)
If you post what usually causes you to lose a game (are you falling behind in production, in weapons tech, in hull size; is the AI expanding too fast or influence-flipping your planets; ...) we might be able to give more tailored advice.