Log into your account at https://poloniex.com/, and select "API Keys" from the drop-down menu in the upper right.
If you see the message "API ACCESS IS DISABLED", click on "Enable API", open your account mailbox and follow the link embedded in the email from Poloniex. As soon as you do this or if there was no such message, proceed to the next step.
Click on "Create New Key". Go to the mailbox again and follow the link in the new email from Poloniex.
And now the API & Secret keys are in your hands.
If you need to delete the key for some reason, click on "Delete" and confirm the action.