Step 1
Login to your Steemit account with the key you typically use.
Step 2
In the top right corner there is a menu drop down box (from you profile pic or name). Click on this box and then click on wallet. Alternatively you can go to https://steemit.com/@whoever/transfers .
Step 3
Make sure you are on the Wallet tab - you will see in the image below that it is underlined in Yellow. Circled in yellow with an arrow pointing to it is the Permissions link. Click on this link.
Step 4
You will see a series of keys - the first one is or the "Posting Key" which is what you want. It will start with the letter "S" if it is showing the public key (as underlined in yellow). Click on the box circled in yellow that says "Show Private Key".
Step 5
If you followed the instructions correctly and everything worked - you will see the private key. In the image below underlined in yellow is the number 5 at the begining of the key. You will know you are looking at your private key if it begins with the number 5 - cut and past this number to your notepad - or whever you need it! You can now logout of your Steemit account.