There are two big steps:  Setting up your account (with a credit card that will not be charged because you are using a $15 promo code that will last three months) and setting up your server.  The screenshots below are about the first task, and the youtube video below is about the second:

https://youtu.be/HoGi-XF8cNk

1. To begin, visit digitalocean.com and click SignUp.

2. You will be prompted to enter your email address and a password. Then you will see this:

3. DO has sent a confirmation to your email.  This is not INSTANTANEOUS – give it up to five minutes. 
This message should NOT be blocked by any spam folders or whitelists (not on Gmail or XEAMS) but later messages may be. This is what the message will look like:

4.  Once you confirm your email, you will need to enter credit card information. 

5. You will again be prompted to authorize your account via an email that looks like this, and again it should not be spam-blocked although it may take a few minutes:

6. You will notice that you did not enter your coupon code for the $15.  You can do that by entering Settings in the top right (as pictured above) and entering your promo code (in the image below you’ll see mine was already accepted):

7. You will then get an email confirming this receipt, as well as the display above confirming it:

8. If you have been receiving these emails, WONDERFUL!  If not, you should check your spam folder, or your spam blocker, and make sure to whitelist the domain digitalocean.com.   Later in the process you will get two emails which, unlike these so far, were blocked (for me), and they contain the root password and instructions critical for doing anything. 

The root password is in the “Your New Droplet” email, and the instructions for your application (e.g. WordPress or Drupal) are in the “Resources for your [Application] Droplet” email.   Below are those two messages in my spam service:

9. Okay, everything else you need can be found in this video (which repeats a little from what’s above, but then continues into creating and configuring your “Droplet”.

https://youtu.be/HoGi-XF8cNk

10. NOTE: This video references changing DNS to create a dev subdomain.  This is useful if team members are logging in to the site after this weekend, because they may not remember the IP address.  Make sure all such team members alter the hosts files on their portable computers to point the dev.domain.com subdomain at the IP address of the virtual server.  Instructions: http://www.rackspace.com/knowledge_center/article/how-do-i-modify-my-hosts-file