YNAB runs completely offline as locally installed software on your computer and doesn't need an Internet connection to run - except to utilize Cloud Sync.
If you already have the trial installed you don't have to re-install the software if you just purchased it. By default all copies of YNAB download as a trial and you only need to paste in your key to remove the time limitation. It also works worldwide. Learn about YNAB's pricing policy.
How does the trial work?
The trial is completely full featured and is only limited by time. It will Cloud Sync with your YNAB mobile app as well as other computers where the trial has been installed.
Download the installation file here and double-click on it once the download is complete.
On the startup screen, click on Start Your Free Trial.
On the next screen, click on Let's Get Started.
Read the Quick Start Guide.
How do I activate YNAB if it's already installed?
Highlight the key from your order email (or look it up here) and copy it - dashes and all - (Right/CMD click and choose 'Copy').
On the startup screen of the software you downloaded from here, click Activate.
Click in the License key field and choose paste.
Click Activate and you won't be prompted for it again.
What do I do after it's installed?
Check out the Quick Start Guide.
Learn more about License Keys.