Warning! This section contains spoilers.
Here, I will reveal some of the strategies I use while playing Space Trader. If players send their own strategies to me, I might also add those.
When starting out as a brand-new space trader, your main goal is to stay alive, and your second goal is to make a profit. Staying alive means that you should never fight. That means that you should avoid fights if you can, and flee if you get attacked. A high piloting skill helps, so my personal choice is to put a lot of skill points in the piloting skill, at least 8, and often 10. Piloting is important for every type of play, so these points are never wasted. To avoid fights, simply don't visit systems where there are "many" pirates or even more than that. If you must visit such a system, because it is the only way to get to a place where you need to go, simply go there with empty cargo holds, except for one canister of water. When pirates attack you, simply surrender and let them have the cargo. They will be satisfied and you won't be attacked again. When you get the cash, upgrade to a ship which has a shield slot and install a shield. From that moment, you may try to visit systems which are a bit more dangerous, because you have some buffer when you get attacked.
To get rich quick, a high trader skill helps but isn't really necessary. Not being a criminal (thereby losing 10% of your trading profits) is also a good thing, but still not necessary. The standard way to earn good money is to pick up water, furs, food and ore on pre-agricultural or agricultural systems, and bring those to a post-industrial or hi-tech system, and ferry some tech goods back. In small systems prices are higher than in large systems, so you best buy at a large system and ship to a small system. Even better is to make use of the special resources which some systems have. While food is a great buy at an agricultural system, it is a lot cheaper when that system has rich soil. Technologically advanced systems pay good money for food, but they pay even better for it if they have poor soil themselves. Furthermore, most government types have some type of goods they especially like. For instance, democracies are populated by free people who like to play games, so games will bring you an extra good price. However, best of all is to make use of special events which occur in a solar system. If there is a crop failure somewhere, ship them food. If people are bored, bring them games or narcotics (if you dare). If there is a lack of workers, ship in machines or robots. In one of my games, I was lucky to find an tiny industrial democracy next to a huge hi-tech cybernetic state. There was a lack of workers in the democracy, so I started shipping in robots. I made a profit of more than 3000 credits on each canister of robots I shipped. I was lucky that the event lasted a couple of turns, and could trade in my Gnat for nothing less than a Grasshopper after about five shipments. And since robots are legal goods, I even didn't have to worry about the police. Of course, this was a lucky find, but there are many such opportunities in the galaxy, not all with such huge profits, but there is good money to be made.
Something which most people find difficult is to get the money to buy enough even to fill the cargo bays of a Gnat. There are several ways around that. First of all, there is a bank, which will loan even a starting space trader 1000 credits, doubling your cash balance. It's best to pay them back as soon as you don't need it anymore, because you have to pay interest (note that interest is detracted from your cash balance as soon as you warp, and is not added to your debt, unless you don't have enough cash), but it's better to get a loan than to fly with empty bays. Another way to get money at the start of the game is simply to sell your pulse laser. This gives you 1500 credits extra, and you don't need it if you don't intend to fight. So, instead of the 1000 credits which most poor traders start with, you have 3500 credits to play with (4500 if you play Beginner or Easy level). Bill Andel suggested selling your Gnat for a Flea at the start of the game. This gives you a lot of money to play with, but you are, of course, restricted to only 10 cargo bays. However, according to Bill, this allowed him to get a Firefly much quicker.
A good buy after the first few days is 5 extra cargo bays. This will allow you to carry even more goods, and they are cheap, so you will earn them back quickly. Just make sure you keep enough cash to buy goods when you invest into cargo bays.
Upgrading your ship is a good idea. You might think it is best to hoard your cash until you can jump from a Gnat to a Grasshopper in one go, but going towards your ideal ship with a few intermediary steps is a good idea. First of all, you usually get more cargo bays which allow you to become a more successful trader. Secondly, you can get extra crew quarters, allowing you to hire mercenaries. If you have a trader skill of 1, try to get a mercenary who is a good trader, and see your profits soar. And finally, be aware that if you become richer, the pirates get stronger and more numerous. While you are still flying a Gnat and hoarding a capital, they will have upgraded and will attack you with all the more power, possibly quickly ending the game for you.
Use the average price list to determine where good deals can be made. According to Andrew Wilkin, if you don't know where you should travel to buy cheap goods, look at the price of firearms. According to him, cheap firearms are a good indication of a system where many cheap goods are available. I myself cannot confirm this observation, but since the determination of selling prices is a complex matter, it is certainly possible that he is right.
When should you take the risk of trafficking illegal goods (firearms and narcotics)? You can do that at any time in the game, but best is to wait until you are at least "lawful". At that point, police won't check on you as often. If they still do, bribe them or flee. Fleeing will revert your police record to dubious, but that still isn't criminal. You will get more inspections, so you should lay low for a few days, until they trust you again. Usually, trafficking is a good thing where profits are concerned. Especially narcotics can bring insane profits if you buy them cheap (at a hi-tech system) and sell them at a very low-tech system. Even pre-agricultural systems will buy narcotics and will pay a lot for them. And if they are a theocracy, all the better.
Concerning equipment, it's best to first fill all your slots before you upgrade to better equipment. Two pulse lasers are better than one beam laser, and a pulse laser and a beam laser together are better than one military laser. The same goes for shields: you better have two energy shields than one reflective shield. Of course, you should decide whether you will invest in better equipment or wait until you have a better ship. Personally, I like to fill all my slots with the weakest lasers and shields and buy extra cargo bays for all my gadget slots, and wait until I have bought at least a Grasshopper before I start buying better shields and lasers. I can't say if that is the best tactic, though. You should know that you will certainly encounter pirate Gnats who carry military lasers (although not that many).
If you want to go pirating, you must have a good piloting, fighting and engineering skill. That means that you need at least one mercenary, and probably two, to compensate for the lack of your own skills. A navigating or targeting system also helps. If the police gives you too much trouble, get a cloaking device. For a trader, a cloaking device is an absolute must. Remember that the success of a cloaking device depends on your engineering skills, so you should rate high in those.
While in the middle game, you are so far advanced that you don't want to lose everything you have built up. That means that you simply shouldn't fight to the death. Be prepared to give up your cargo to a pirate if you are in a losing fight. Yes, it hurts, but it's better than being killed, or having to eject your escape pod. Of course, when you are a psycho and the police is attacking you, you might not have the option to surrender. But such is life on the road to hell.
When you are flying a Wasp or Termite with all military lasers, reflective shields, a couple of nice gadgets and some supporting mercenaries, the endgame has started. If you held out so long, congratulations. Still, it's not the time to let your guard down, because even a Mosquito can kill a Wasp if the Wasp is weakened by earlier fights. The richer you are, the better equipped your opponents will be.
If you want to end the game the way it should be ended, you should seek out someone who is willing to sell you a moon. There are several solar systems where a moon is sold, but you will only get that offer if you are worth at least 400,000 credits. So the offer might be in a system which you visited before. Just start coasting through the galaxy, carrying half-a-million credits in cash, until you get the offer. It is not wise to sell your Wasp for a Gnat, thereby creating the money you need to buy the moon, because the costs of the moon are part of your worth, and since you still have to traverse part of the galaxy to claim your moon, you will need your ship to fight off all the strong pirates you'll meet underway.
Claiming your moon ends the game. Congratulations. Now it's time for a harder level.