Merchants are a guild composed of traders. They are also a faction whose ships (Tarsus, Galaxy, Ulysses, Drayman) you can encounter from time to time. Their ships remain gray even after installing a B&S radar, but this isn't supposed to mean the likewise gray uncontrolled systems are somehow afiliated with Merchants.
On most planets (including Basin, where you start) the guild is a small room with a terminal and a Guild Master behind a counter. You use the terminal to browse and accept business opportunities, but this is only possible after you've joined the guild for an entrance fee by talking to the Guild Master:
"Hi, how are you? I'd like to invite you to join our guild. We don't supply you with merchandise -- you'll have to buy that yourself -- but we do offer you very favorable deals for your merchandise. It will only cost you 4000 credits to join our ranks. How about it?"
After accepting you start out as an 'iron' level member and the terminal shows you 4 different missions for consideration. Over time, or when you accept one, they get replaced by new choices. After successfully completing a number of missions your member level rises to 'copper', 'steel', 'bronze', ... which means you get more possible choices shown at a time. Your level can also decrease if you accept a mission but then fail to complete it in time.
Newly generated missions take the size of your current ship's cargo hold into account. However, you have to buy the commodities yourself and you may not have enough money to acquire the goods a particular mission calls for. As a rule of thumb, if a mission offers a certain number of credits upon completion, you will need to invest about half that sum to purchase the required commodities first. The other half will then be your profit.