When you first log in, you will see a green button underneath the area for your profile picture. It's on the left side of the screen and says "Upgrade Subscription." Click it.
You will be taken to another screen where you will see another big orange button on the left side of the screen that says "Get Plus Now".
Once you click "Get Plus Now" you will be prompted to put your code in. Type in your code and press Enter.
Next you may see a secure payments portal where you can enter in your credit card information to complete the purchase. Your promo code will be automatically applied from the previous "Have a promo code?" form.