As KDE produces Free Software, you can download and install KDE programs in most cases free of charge. On this page can read below about various ways to get KDE software.
KDE software consists of a large number of individual applications, Plasma, a desktop workspace to run these applications, and KDE Frameworks, a set of libraries they are build upon. You can run KDE applications just fine on any desktop environment. KDE applications are built to integrate well with your system's components. By using also Plasma, you get even better integration of your applications with the working environment while lowering system resource needs.
Plasma runs fine on relatively recent PCs, but they will also work on older machines with more constrained resources.
Trying out a desktop workspace can seem a daunting task. Installing Linux or BSD requires a commitment that you may not be quite ready to give yet. KDE provides a list of resources for alternative methods of trying a KDE desktop and applications, some of them without even needing to have Linux or BSD installed.
Installing Plasma on your system is easy if you use the major Linux distributions; it's included in nearly all of them! A partial list can be found here: Distributions Shipping KDE Software
There are instructions available for building the source code. Building from source code is not recommended for normal users as it requires knowledge of software development tools.
KDE applications run fine on most Linux, BSD systems. In these cases, the recommended way to install a KDE application is to use your operating system's software management tool to install it. It comes included with most Free operating systems.
The KDE Frameworks are a set of libraries built on the Qt framework, providing everything from simple utility classes to integrated solutions for common requirements of desktop applications. You can download them at http://download.kde.org/stable/frameworks/ or read the online documentation.
KDE software on these Operating Systems is in experimental state. Things might, or might not work properly at this point in time, largely depending on the app in question.
An installer for KDE applications on Windows is available on windows.kde.org. These are experimental packages. On TechBase you can find detailed installation instructions.
For Apple's OSX, there are technology previews of some applications available on mac.kde.org.
KDE provides some software for Android under the KDE Community account on the Google Play Store.