Ada is a programming language for which there exists multiple compilers.
One of these compilers, and perhaps the most used, is GNAT. It is part of the GCC toolchain. It can be installed from several sources:
The yearly GPL release done by AdaCore, available for free on libre site. This version has undergone all internal testing that AdaCore does for its pro releases, is available on a large number of platforms. The compiler and its runtime are released under the GPL license, and, unless you are using no runtime, any executables you distribute will also be covered by this license. For academics and projects in their initial stages, this is not a problem.
The FSF gcc receives the same patches regularly. The version of GNAT might not be always up-to-date, but catches up regularly.
A number of contributors are packaging that FSF version for various Linux distributions (Debian-based systems, among others) and binaries for Mac OS X. Using the package manager from your distribution might be the simplest way to install GNAT. Such versions come with the standard GCC license, and allow you to write closed source code.
AdaCore also provides GNAT Pro, which comes with the standard GCC license which allows you to write closed source code. More importantly perhaps, it comes with support, should you have questions on the use of the language, tools, how to best implement something, and of course bug reports and enhancement requests.
Another number of compilers are listed in the Ada WikiBook, together with installation instructions. Getadanow.com features editions of FSF GNAT, ready-made for various operating systems on several types of hardware, or virtual machines. The site also collects resources for learning and sharing Ada.