I recommend using the unofficial MoO patch that is stickied at the top of this forum, but it is not a required thing. There are some nice additions to the interface which make some things easier to follow, such as being able to review the descriptions of previously researched techs on the tech screen by clicking on them, and other little things (like the starting ship cost bug being fixed, so that you don't have to redesign your scouts and colony ships to cheapen them).
One thing that might be helpful to know is that natural population growth follows a sigmoid growth curve, which means that planets start out growing slowly, grow the fastest when they are about halfway full, and then level off as they reach their max population.
Another thing that you absolutely need to know to really play the game (and which I WISH was explained in the original in-game interface!) is that technology comes in "rungs" every 5 levels. So, levels 1-5 are the first "rung," levels 6-10 are the second "rung," etc. You will need to research or acquire at least one technology in each "rung" to unlock technologies in the next highest "rung" (and actually, your starting level 1 techs don't count towards the first rung, so you'll need to research something in levels 2-5 to advance to the second rung). You are guaranteed to be able to research at least one technology in each rung, and sometimes you will get more than one option in each rung if the RNG is being kind to you. Which tech(s) you get the option of researching are entirely random each game, which forces you to adapt to what the tech tree throws at you.
So, for example, here is the weapons tech tree:
http://strategywiki.org/wiki/Master_of_Orion/Weapons
(I recommend keeping these tech pages open as you play, as unfortunately the in-game interface does not show you this information ahead of time).
You see that, for the first rung (levels 2-5), there are the following possibilities:
*Level 2: Hand lasers
*Level 4: Hyper-V rockets
*Level 5: Gatling lasers
(Notice that there is no level 3 tech. This is not a typo. It is typical.)
In any particular game, you MIGHT only get the option of researching hand lasers in the first rung. Or, only Hyper-V rockets. Etc. OR, you might get lucky and have the option of researching 2 or 3 of those above. If you pick one between your options in this case, the option to research the other one(s) at a later time remains, although you will then also get the option of moving on to researching a "2nd rung" tech, such as:
*Level 6: Anti-missile rockets
*Level 7: Neutron pellet gun
*Level 8: Hyper-X rockets
*Level 9: Fusion bombs
*Level 10: Ion cannon & Heavy ion cannon (you basically get two weapon types for the price of one if you research this).
In any particular game, you might have only fusion bombs for options for your 2nd rung techs, or only neutron pellet guns, or maybe 3 out of the 5 techs as choices. It varies. In any case, once you research one of these "2nd rung" techs, then you can research a "3rd rung" tech (Levels 11-15), or you could go back and research any 1st or 2nd rung tech options that you were given that you passed up on before.
As you research more techs and higher-level techs, your "tech level" increases. This is the number over on the right of the tech screen next to each category. As your tech levels increase, previously-researched components in those categories will become cheaper and more "miniaturized," meaning that you will be able to pack more of them onto ship designs. So, sometimes it still pays to outfit your ships with obsolete components because they will be cheapened and you will be able to fit more of them on your ships. It depends. Ship design is really where the most fun is at in this game, in my opinion.
That's about it! The rest you can probably figure out as you play the game. Good luck!