At the very beginning of the game, you will get your first coin for completing the tutorial and picking up the coin that is in that level.
Immediately afterwards, as you cross the bridge, talk to the NPC, and he'll give you three coins.
Run 'N Gun levels
The bulk of your coins will be gained from the Run 'N Gun levels. Each Run 'N Gun level has a total of five coins that can be collected. There's six of these levels, totaling 30 coins. For the most part, these coins are easy to find, and the most important thing is to have enough skill to beat the levels.
A gingerbread girl in World 2 will give you a coin if you take the shortcut. In order to take the shortcut, walk behind the birdhouse and behind the mountain all the way around to the dragon tower.
A juggling gingerbread boy in world 2 will reward you with a coin if you get four parries in a row without touching the ground.
There are some easy ways to parry four times, like in this example.
The final four coins are hidden in the open world. There is a single coin for each area in the game.
On Inkwell Isle One the secret coin is placed behind Axe NPC in the trees. He won't move until you beat each boss in this world, so make sure to check this place before leaving.
On Inkwell Isle Two travel to the very center of the map close to the exit of World 2. You'll see a small greenish cabin. Grab the second secret coin behind it.
On Inkwell Isle Three you will find the third secret coin behind the ticket booth that is near Cala Maria Boss.
And finally, the fourth secret coin can be found in the Casino behind the wall on the left-hand side of the door. Now you can take your coins to a Porkrind's Emporium and finish off buying every upgrade in the game.
I'm also going to show you how to get all 16 of the gold coins in The Delicious Last Course DLC world. Getting all of these coins will allow you to go to Porkrind's Emporium and buy all of the DLC items, including the three weapons, the charm, and the Broken Relic.
First of all, complete the tutorial to learn Ms. Chalice’s new tricks. Follow the instructions on the screen and the first coin will be yours! After all, you’re better than that journalist who couldn’t get through the Cuphead tutorial, aren’t you?
If you have completed the main game, you can talk to the newspaper boy, and he will thank you for helping to clear the islands of villains and reward you with three gold coins.
Just like in all the worlds of the main game, there is one secret golden coin hidden on the new island. To find it, you need to go behind Porkrind's Emporium and move left along the hidden trail by the mountain hills. The golden coin awaits you at the very end of this path.
And finally, to obtain the remaining coins, you will need to complete a series of stages called The King's Leap, scattered around the map. You will have to climb up ladders hanging from the sky to fight against five chess pieces. For each victory, the King will reward you with a couple of coins, and for the last one - with three. Thus, by completing all the King's challenges, you will be able to earn 11 coins.