In 1v1:
Organization, or rather the lack of really affects how well one does. I've seen and played countless games where a player with superior forces or some other advantage throws it out the window because of the lack of proper fleet management. If you take a close look at my game over screen shots, you'll notice that in most 1v1 games I play and win, my population suffers heavy loses. However, I still manage to overcome those heavy loses mainly because at the end of the game, I'm left with a far larger naval force and am free to do as I please.
A couple of points about how to be organized:
- Deploy your fleet in the same manner you would silos. That is, each ship should be able to support another or be supported by another as much as possible. Don't leave large numbers of ships stranded or cut off from land/naval support. Scout battleships are the exception.
- When using scout battleships, don't set 5 of your battleships on top of a single enemy scout. What will happen is you'll kill one ship only to find subs underneath yours and be immediately at a disadvantage. On top of the loss, the enemy will now have even better intel on your navy.
- During the course of the game, don't allow your fleet to become scattered and cut off from the rest of your forces. This is akin to an infantry breaking its lines. That usually means defeat. If your lines are broken, reform them quickly.
- Use ships in a manner that complement each other. For instance, I've noticed that many players follow the rule of carriers behind battleships but keep their carriers too far behind to be of significant help.
Here's an example of the last point. Take a look at the fighter range difference. The top group is what I typically see, carriers stuck way back. The picture shows the immediate difference in the range. If you stop and think about this, the top groups fighters have to use up 60% of its fuel and range just to get to the front line (bb's). By the time it can engage the enemy, it's almost out of fuel. On the other hand, the rest of the group can almost immediately engage in the battle. Fighters have the smallest radar range of them all and must almost be on top of enemy ships to start shooting at them if they are the eyes of your fight.
In 1v1, please don't empty out every fighter from your arsenal. That is completely unnecessary. It becomes even more wasteful when, as I typically observe, they are left to fight the battle themselves. Seeing 30 fighters being launched arbitrarily and then left to fly off with no further instructions is just mind boggling to me. What a waste.
Something else that I'd like to mention. See how the four bombers are traveling north/south? That is the correct way to launch bombers for naval battle. Parallel to enemy ships and behind the protection of battleships. The bomber heading directly into battle is what I see more often. It will almost certainly die a miserable fiery death before it can do much damage.
With regards to staying organized... The picture also shows how to group units together. Use the combo of carrier/battleship as this allows for the best use of both ships. They can support each other much more effectively this way. While the game is being played, the original groups should stick together. Also, don't forget to use the airbases to support your navy. Remember, an airbase stops making fighters when it has 5 on the tarmac. As soon as you use one from a carrier, there should be another on it's way from an airbase to replace it, at least at the start.

When using bombers to kill surface ships, either re-direct your bombers back behind your battleships when they reach the edge or move your battleships along with the bombers to keep them protected. Too many times I've seen bombers lost because they started out protected, but ended up away from that protection.
Lastly, keep your navy fluid. When the enemy discovers your location, move. Make the enemy guess every single time where you might be, don't give them the advantage of a static position or area.