Elite dangerous is a space-based futuristic MMO game, with 400 billion star systems and various factions both major and minor battling for power. There are a multitude of ways to play the game, where is a list of them.
[*]Explorer: Considering that there are 400 billion star systems in the Milky Way Galaxy, there is a LOT of uncharted space. So if you've got the money for a long-range ship with plenty of fuel, a fuel scoop, and a powerful discovery scanner and surface scanner, you can go out into the galaxy and explore parts of space previously uncharted. Sure you may find lots of celestial bodies that were discovered before, but don't lose heart, because if you put enough time into it, you will find a few systems nobody has ever been to, and whenever people go there, they will know you found it first. Once you're done exploring, you can go to a station in civilized space and sell your exploration data for lods of emone.
[*]Trader: Buy low, sell high, get rich, that is the goal of a trader. You buy food and water cheap from agriculture stations, sell them high on extraction stations, buy metals and minerals cheap on those stations, sell high on refinery stations, buy agricultural equipment low on those planets, and sell high on agriculture planets. Repeat the cycle as many times as you want to maximise your profits. Of course you can buy and sell other things, just try to make sure you don't accidentally buy high and sell low.
[*]Smuggler: The dark twin of traders, they buy illegal goods where it is legal, and sell them where it is illegal for their own profit, they must watch out for police and military forces trying to stop them, as a cargo scan will result in a large fine, depending on how much illegal stuff you have. Watch out for pirates too.
[*]Miner: These guys are practically the backbone of space society, as they mine valuable minerals and metals with their mining lasers, process them on the ship, and sell the refined product to stations. They have to watch out for pirates though, the last thing you want is an anaconda cargo scanning you when you have a cargo hold filled with gold.
[*]Pirate: Arrrr, these scurvy dogs be the scourge of the galaxy, plunderin' miners and traders for their precious booty. They be on the lookout for police and bounty hunters, else they rest in Davy Jone's Locker.
[*]Bounty Hunter: These guys hunt down and try to destroy pirate ships, not for the protection of others, but for their own profit, this is a dangerous job however, as pirate ships are often well armed, and often in groups. However, the pay for the bounties is often well worth it.
[*]Mercenary: Mercenaries are soldiers for hire, they go to systems in the midst of war or civil war, go into conflict zones, pick a side, and begin fighting, each ship killed grants a combat bond, which can be turned in for cash, watch out though, if you end up surrounded by hostile ships you're dead, and you lose all your bonds.
[*]Assassin: Cold hearted killers, these people take the jobs of killing high value targets for money, whether it be massacring several ships belonging to a certain faction, or eliminating a single target, these people get the job done, or die trying.