To create a corporation, you must be level 20. The cost to create one is $300,000
To begin with, your corporation has 5 slots. Every $1,000,000 of mission earnings within your corp will unlock a new slot, up to a maximum of 15 members. Inviting a player will cost the owner of the corporation $25,000, from their personal balance.
To take over a trader, your corporation must be the primary traders at this spot, the trading ui window will show the % of the market that each corporation has. Controlling a trader will increase your corporation balance, based on how much others use this trader while you control it, and allows you to start a production boost there.
Production boost removes the inventory cap at the trader, and increases the production speed for 10 minutes. This can only be done when your corporation controls the trader that you want to boost.