You unlock the Merchant rank after making approximately 3,760,000cr of profit on items sold in the Commodities Market.
Profit from selling items through the Black Market does not appear to have any effect on your progress towards Trade ranks, so make sure that items you purchase are legal at your destination.
To increase your gains, build out your ship for speed and cargo capacity. I am using a
Cobra Mk. III built out for both trading and exploring*, and haven't had any problems evading interdiction. The Cobra is a bit pricey if you're just starting out, but it's worth it for the combination of potential storage space and speed. If you do get yourself yanked out of Supercruise, you want to be able to get away and recharge your FSD as quickly as possible.
Thankfully, finding profitable trades isn't entirely a crap shoot. There are tools like
the Elite Dangerous Database(EDDB) which generate trade routes based on data submitted by users. There are few options for route finding, with the easiest being Loop Routes (you only have to remember two destinations, and the commodities to buy at each), and the most profitable being multi-hop routes. Slaves and Imperial Slaves are almost universally illegal goods, so make sure to exclude them.
*Note that if you're just focused on trading, you can keep an additional 4 capacity Cargo Rack in place of the Fuel Scoop, but if you head off to a profitable trading route far away, you must make sure to find fill-up points along the way. You don't want to get caught deep in uninhabited space. The
Fuel Rats aren't
always available, and instancing on Xbox Live can interfere with their ability to help.