Windows
The Windows package of Celestia is a self-extracting archive. Download it to your computer and then run it.
macOS
The macOS package for version 1.6.1 is a disk image. Download it to your computer, double click it, and follow the instructions in the README. The package for 1.6.2 is a zipped bundle, download it and unpack.
GNU/Linux
See the installation instructions for your distro at the below pages.
Source Code
Celestia is an open-source project. As such, its source code is provided and is freely modifiable and redistributable as per the GNU Public License. Installation instructions are provided in the INSTALL file.