The JUCE library is quite definitely not free. The good folks at Roli Ltd. do, however, offer two free options (“Personal” and “Education”) which allow people to get started with JUCE without having to pay for a commercial license, and these options involve certain conditions to which you'll have to agree, whether you like it or not. This page gives you a chance to preview the whole process before you start, and gives some hints one where to put things on your PC or Mac.

The very first time you run the Projucer, the first thing you'll see is this rather scary thing:

This makes it pretty obvious that you aren't going to get any further unless you sign up for a developer account with Roli. Relax. This is painless, and free, and will also allow you access to Roli's online JUCE forum at https://forum.juce.com where you can get answers to questions as you learn about JUCE. If you haven't done so already, you can click on “I do not have an account” at the bottom, and you'll be presented with a form that looks like this:

After you fill in all the fields, scroll down, click the “I would like to receive the latest news from Roli” if you wish (I like the fact that this is not checked by default—thanks, Roli), and hit the big green Register button, you get this:

You have to check the “I agree to the privacy policy and JUCE 5 EULA” to go any further, so now would be a good time to review them by clicking on the links. Both are pretty reasonable. Once you do check the “I agree” box, the four license-option buttons appear—click on Personal, and then you'll be able to click on the “Continue” box at the bottom, wherupon you'll see this page:

Click the “START USING JUCE” button at the bottom, and you'll finally be able to get started… Whoops! Nope, one final hurdle:

Once again, you don't really have a choice, so click OK, and finally you can get started with the Projucer.