Here are simple steps to obtain the Shopify API key.
Step 1:
Log in to your Shopify admin account: https://www.shopify.com/login
Step 2:
On bottom of the left hand side of the dashboard, select "Apps":

Step 3:
On the top left side, select "Private Apps":

Step 4:
Then select "Create private app":

Step 5:
Specify the tile of the private app and provide a contact email if necessary:

Then select the necessary permissions:

Once these are done, select "Save app".
Step 6:
After the app is saved, you will be able to review it.
Authentication details will then be provided:

You can simply select the "Cancel" button once you are done reviewing these.