Trade rare commodities.
There's a web tool I've been using, I'll link later I've got it bookmarked at home, you have to do long 130ly+ trips, which is hard in the basic ship. But the payout is a lot higher than any regular commodity.
Or if you're good enough you can go pirateing/bounty hunting.
Mining is another option, but pirates prey on you more often than as a trader.
Exploration needs a good couple of million credits dropped into it to get the most out of it. Though if you wanted a lower return you could explore in the basic ship.
Bulletin board cargo runs we need four of these moving/procuring is the way I made enough to buy my second ship (before I'd discovered the rare commodities) because they're paying a higher rate for normal cargoes, and the times are usually quite generous.