Where the money is
Your gold sits in the footer of your bags, next to how much you are carrying.
It comes from monsters, from the people who give you work, and from dungeons and portals, which pay everybody who finishes them. You can also sell what you no longer need to a shopkeeper. It goes on food and potions, armour, the tools of the trades, more room at the bank, and one day a guild of your own.
Everything takes up room
A bag is a grid, and every item takes its own shape in it. A bow takes more room than a ring, so what you carry is something you have to choose. Weight counts too.
When your bags are full, the bank is where the rest goes.
The bank
The banker keeps the bank in town. Your first drawer costs nothing, the bank does not care what things weigh, and what you leave there stays there whatever happens to what you are carrying. More drawers can be bought with gold, which is a good reason to save some. The details are in the bank.
What to keep and what to drop
Keep anything you cannot easily get again. Sell or drop anything you are carrying out of habit. The ground is a real place: what you put down stays there for a while, so you can go back for it if you change your mind.
Passing things on
Stand next to a friend and open a trade to hand them items or gold directly, or post it to them at the mail counter and it waits until they next sign in.
More on what there is to do with it: quests.