It seems like you're having an issue wrapping your head around the turn based nature of the game. For now, that's what I'll tell you about.

The turn button is used when you've finished moving your ships, setting what to build in your plants and starports, setting your research goals, and setting your funding levels. Until you click it, nothing happens. That is, your ships don't refresh their movement, no research is actually completed, nothing is acutally built, etc. When you hit the turn button a 'week' automatically goes by while the people of your empire do all the things you ordered them to do during your last turn.

An example of the first few turns:

Double-click the flagship and check the box 'auto-survey' so that it will automatically go find the bonus items.

Click the colony ship and right click on a star system with plantes in the mini-map at the bottom right so it starts heading towards a possible second colony site.

Double-click your planet. Double-click on a factory, and then buy, and then the first option, so that by your next turn you will have speedbuilt.bought a factory and instantly upgraded your production potential.

Click on build ship. Choose a colony ship. Hit buy ship so that next turn you'll have a colony ship ready to explore and claim an additional planet.

Click on the triangle button and adjust the tax rate slider so the approval % is 100%. Adjust the prime spending slider so you aren't hemmoraging cash. Reduce the military spending slider because you're trying to build up your colonies at first, and you're buying your initial ships outright instead of building them.

People will disagree with points on a strategic level, but that's often what a first turn will look like.

Okay...thanx...now I understand what I was doing wrong! I was clicking the Turn button after making every single setting change, such as when I chose a tech upgrade, or added a factory. I should go thru every menu and make whatever decisions I want on all of them first and THEN click the Turn button, right?
Must I or should I wait any specific amount of time or for some type of event or notification after clicking the turn button before choosing my next series of changes/moves? Or does the game instantly update itself and I can play as fast or slow as I want to?

Right.

As soon as the turn button becomes visible again it it your turn again. In the early game it is almost instantaneous.

You can take as much time per turn as you need. I don't time myself but I am sure that some of my moves take a half hour or more and some take seconds.

1. Pick the technology you want to research. I normally start of researching engines so I can get better range out of my ships.

Engines don't give range. Life support does.

You can play as slow or fast as you please.
If need 5min or 1 hour for a single turn doesn really matter. (exept that you are going to have a VERY long game if you need one hour for every turn)
And yes you should go though every menu the first round to give orders.
However it is not necassary to do this every round.

Example for first round/ turn (plz read the various other threads about whats best in first round)
Lets say you ordered you home planet to build a factory and a colony ship.
You ordered your labs to research advanced propulsion.
You set you spending to 100% and you taxiation to 45%.
Now you move your colony ship to the nearest planet which has a higher PQ than 0 and move your flagship towards the nearest anomaly.
Thats all for round 1 so you press end turn now.

The second round/ turn (called week in this game) starts now
You will see that the amount of time you need to produce the factory and the colony ship is now reduced by one since that spend the last week working on it.
The time to research propulsion is no also decreased by one.
Your ships will now have full movement again so can send them manualy further towards their goal
or if send em to a destination they couldn't reach in the first round they will use their movment points automaticly at the end this turn (2)
SInce your colony is already building something it is not necassary to go to build menu in this round
Its is also not necassary to go to the research menu this turn because you are still researching propulsion.
Also it is not necassary to change your taxiation or your spending.
So you will most likly only move your ships in this round .
End turn

Start of round 3
depending of you adjusted your spending sliders (plz see other threads again)
it is possible that your colony ship AND/ OR your factory AND/ OR your research is finished now.
So you will move your ships this round.
If you researched a neew tech you will visit the tech menu to give new orders.
If you build a factory you will visit your planet to give a new building order.
if you finished your new ship this round you will give new building orders to your shipyard and order this ship to move.
Maybe you even colonize a new plaent this round so you will give your new planet building orders.
After you have done everything you thing is necassary you press end turn and the next turn (4) beginns

Short:
you can visit every menu every turn as many times as you plz without penalties.
You dont loose money or (virtual) time, but you will play a long (real life) time if you check everything every round.
So if need to think about samething take yourself time, the game isn't rushing you.

I hope this helps

I just want to thank everyone for jumping in with your expertise. I've played strategy games in the past, but they were all real-time, and this will definetly take some getting used to. But I also think it will be worthwhile because it makes the game more like chess in that you're not being rushed and you have the time necessary to really think and plan as you play the game.
I started a game yesterday, which I'm now going to start over from the beginning, in which I chose the terrans, and had only three other races to deal with. One is a pacifist race, one a war-like race, and another subserviant to the reigning powers that be. I figured that would introduce me to a good range of tactical considerations! I also chose a small galaxy and put it on beginner's level until I really knew what I was doing.
It's too bad there's no multiplayer available though, as I can see a lot of potential in something like that!

Basic Stategy Guide in Databanks from above: Link