It's actually pretty straight forward #h5yr!
First you'll need to create a Disqus account and then secondly you'll need to let your Umbraco theme know your newly created website shortname.
Go to https://disqus.com and Get Started.
Signup with Facebook, Twitter, Google or your email address.
This step is very important. Make sure you choose 'I want to install Disqus on my site'.
Create a website name.
There are paid plans you can setup but for now select the FREE plan. You can use this forever.
Ignore the platform setup. Click on 'Configure Disqus'.
Enter your website name and then 'Complete Setup'.
Choose to 'Dismiss Setup'.
You will now be on the Disqus dashboard. Click on the top navigation item, 'Settings'.
Locate your website Shortname. Copy this name.
Login to your Umbraco CMS > Navigate to your blog in the tree menu > Click on 'Blog Settings' > Paste your website shortname into the 'Disqus Username' field > Save and Publish