Gratuitous space battles is a game many people play, but few get really good at. I am fortunate enough to have played against some of the best people around, and have adapted my strategies until they could beat virutually all challenges on the most difficult and most attempts lists. This is a summary, not of how to build ships, but how to think about ships.
Cruisers:
These are the backbone of your fleet. The biggest mistake i see people make is cutting cruisers. Fighters and frigates are nothing but support for these bad boys. Know how to make a really good cruiser, and you will win. The key here is versatility: your cruiser can beat one thing, but can it beat all the rest?
Frigates:
As the mid range ship, these leave the most room for creativity. However, the first rule of frigates is this: if you are basing your fleet on cruisers, do not use them. These are to be used where cruisers are limited: either the budget is too low to allow more than 3 decent-size cruisers, or cruisers are disabled, or some other effect. If you are extremely good they can be made to fight cruisers, but in the end a well built cruiser will always win against these pound for pound in a large battle. Within the arenas they are useful, there is a massive amount of diversity. Experiment with different combinations of range, speed, defences and firepower to see what works best.
Fighters:
Fighters have two main uses: In fighter-to-fighter combat, and as extra damage per second against cruisers and frigates. As extra DPS, they excel, but beware of high-resistance defences. Small fighter weapons will bounce off many defence systems, but if supported by heavier weapons they can make mincemeat of otherwise nearly unbeatable fleets. As dogfighters, they are fighting their own kind. Here refinement is the watchword. You will win and lose dogfights by margins of 5 or 6 points of health, because a minor advantage multiples out over time with such small ships.
General tips:
The way to make yourself good at building ships is an adaptive process: make one, then play it against an enemy. It will lose. You will then modify it so it wins. Repeat (series of challenges with other players are very good for this). Also, feel free to copy design principles from others, but never try to replicate someone else module for module. You will only ever be 95% as good as them, and that isn't good enough. Always try to improve on others work.
On positioning, many people will put out fleets that use decoys to foul your lines or drag you around the map. This will make you curse a blue streak. I advise against positional tricks of your own, because they are so easy to counter with another positional trick. For example, a common decoy tactic might be countered by a fleet set on the other end of the map, but then your opponent could just move their fleet to your end and win that way. I advise instead to counter the positional trick with a relatively small group of units, and leave the rest to their business. For example, send a group of 4 extremely fast frigates or 3 fighter squadrons to run down that decoy before it has much effect, rather than changing the deployment of your entire fleet. If your opponent redoes his fleet in a different way now, you have only lost the few countering units rather than your entire fleet.
Many people will find ways to break the game. They will find a trick that lets them deploy ships one on top of the other, for example. One guy has found a way to put cruiser modules on a fighter. These people will always be around, and will always be nearly unbeatable, even if unskilled otherwise. If you can find a trick like this, good for you. By all means, post a challenge of it. Do not however base all of your challenges on it, as that will only make people angry. Also, for heaven's sakes, never give out your secret. I do not want the game to become a matter of who can find the most overpowered bug, and i don't think you want that either.
Finally, never try to work your way up from easy challenges to hard. Go straight for the hardest challenges you can find, save those that cheat. When I first started playing, i played a challenge with over 100 losses recorded for every win about 10 times. From that one challenge, i learned a style of combat that let me beat 80% of the challenges i found until the parasite expansion came out and changed the game. Only be getting your ass repeatedly kicked will you get good enough to kick others' asses.
Now go, and get good at this game.
I need more opponents.