Windows
The Windows package of Celestia is a self-extracting archive. Download it to your computer and then run it.
macOS
The macOS packages for 1.6.2 and 1.6.3 are both zipped bundles, choose your version, then 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.