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There are several paths a player can take to generating money within Endless sky, these main methods are listed below. The three earliest careers you are introduced to, are: Cargo Trading/Delivery (Star Barge) People Transport (Shuttle) and Pirate Looting. (Sparrow)
Delivery & Transport
Transport, a respectable job, gains profit from picking up people from someplace, then dropping them off at another. Transport missions, both cargo and passenger, are absolutely the best way to gain money in the early game. Click the Jobs button, which shows the Map screen in Missions view. Rush deliveries and tourists usually offer the best contracts, but not always. If you're lucky you'll find passenger and cargo jobs to the same system. Be care Collect higher paying missions as you go will help you fund a Heavy Shuttle, maybe a few more normal shuttles too.
Cargo Trading is a rewarding job, if done right. Use your time to jump from one place to another, buying and selling goods for profit. Trading is a low value proposition, but very important at the start of your career. Know a good trading route and have a Drak's worth of patience? This is the job for you. After accepting any good transport missions (see above), go to the Map screen in Ports view. Click the systems on your mission route (or just nearby ones if you don't have missions) and look at the trading box on the left. Trade the commodity you can get for a low or very low price and fill your remaining cargo space with it, then go to a system who will buy it for a high or very high price and sell it there. There will always be something that can help make ends meet.
Taking out merchant ships is a very dangerous job, reserved for only the best of pilots. If you're trying to loot merchants, you need to have very high damage weapons to take them out quickly, then lure away the defense force so you can board and grab the cargo. Auto-fire is very useful to prevent destroying the target, and weapons like the Ion Cannon and Flamethrower that disable the target rather than damaging it make this strategy most effective.
After you have taken all the cargo you can, run to another system which isn't after your guts and sell it all to repeat. Playing this way with the Republic and other governments won't make you a very popular person, and may even result in you getting shot on the spot.
Death and Destruction!
"The best way to earn money! Disable some weak arse pirate then swipe their ship from under their noses! Then amass an army to capture bigger and more awesome vessels of destruction! Or just watch your poor little ship get blown to bits!" This can be a more exciting way into the game, as you'll have more cargo space to make better money from trade routes and missions. You can take on assassination missions too, which pay well for you to take all the souls on those ships to hell.
Crippling enemy ships and selling loot is the most effective way to make money in the mid & late game. Once you've upgraded to a more powerful ship, make your way to systems within a few jumps of pirate planets. Stop firing when the targeting scan turns gray, then board them. The game helpfully displays outfits and cargo in order of best price-per-ton. Click the Take button until your hold is full.
Capturing enemy ships whole can potentially pay even more, but it definitely has risks. You need enough crew to win the fight then fly both your flagship and the captured one. Plus you can only sell ships at a planet or station with a Shipyard. If you're in hostile territory, a few hits might destroy the captured ship before you get there.
Note: NPC ships like the local Navy will almost always destroy enemy ships within their range, so try to cripple pirates far out from the system center so you can loot them undisturbed.
Once you've racked up enough kills to advance your reputation, you'll start seeing Escort contracts in the Mission list. Immediately after departing the planet, seek out hostile ships and stop them before they can attack the ship you're escorting. Getting an escort contract to a system where you're already heading can be like free money. Sometimes these convoys your escorting attract some pirate attention, so fights will be more frequent.
Bounty missions are inconvenient because they require you to visit nearby systems looking for the targeted enemy, but they're the highest-paying contracts in the game, and the loot from crippled ships is almost always very valuable. Most times, these ships hide in systems that aren't travelled very often. Like Ilidaria in the Free Worlds sector.
Mining is a very simple process, simply fire at ore asteroids (they tend to stand out) until they are destroyed, then pick up their bits and sell them. The ore appears under the "Special" section in outfitters, and fetch a fair sum of money for the patient miner.