There is 3 great way to get start : trading, exobiology and exploration but first you'll need a fited ship and this require money.
Easiest one is exobiology, by using great tools like Inara or a pre-defined Elite Dangerous Star Map road, you'll make millions in just an hour BUT you'll need the odyssey extension and the artemis suit. (having a fuel scoop on your ship is advised).
If you got the default elite, equip your sidewinder with a fuel scoop and a detailed surface scanner, by scanning earth like words you'll make quit some money again you'll need Inara or a pre-defined Elite Dangerous Star Map road.
Finally if grind don't afraid you, take goods from point a to point b, using inara to know what goods is sell at a lower price and then were it's best sell in a reasonnable near distance 10 to 40Ly. For that you'll need to clear all unecessary equipment on your ship to equip cargo racks and when you got sufficent money change your sidewinder to an adder then a type-6 then type-7 and finally type-9 (type 10 is "made" for xeno-hunting) always keep a shield till you'll get confident enough to fly without one. As you get your type-9 you'll seek agricultural station with expansion state as they'll provide you some 50.000.000Cr contracts making your profits fast and safe. (only use bertandite, indite, lepidolite, gallite, coltan and uraninite "mining" mission then go to the nearest mining station and buy those materials)
